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Techniques for high-speed direct modulation ofquantum dot lasersYan Li

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Yan Li Candidate Department of Electrical and Computer Engineering Department This dissertation is approved, and it is acceptable in quality and form for publication on microfilm: Approved by the Dissertation Committee: , Chairperson Accepted: Dean, Graduate School Date

TECHNIQUES FOR HIGH-SPEED DIRECT MODULATION

OF QUANTUM DOT LASERS

BY

YAN LI

M.S. Optics, Sichuan University, 2000

DISSERTATION

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

Optical Science and Engineering

The University of New Mexico Albuquerque, New Mexico

May, 2008

iii

ACKNOWLEDGEMENTS

My deepest gratitude is to my advisor, Prof. Luke F. Lester. I was fortunate to have

his support to continue my research in the semiconductor laser area. His guidance,

perspective and encouragement are always a major driving force for me to fulfill my

dissertation and will benefit my future career. I really appreciate his infinite

understanding and patience during the last four years.

I also would like to thank Prof. Kevin Malloy, Prof. Christos Christodoulou and Prof.

Sudhakar Prasad for being on my dissertation committee and for reading and commenting

on my thesis. I have special thanks to Prof. Ravi Jain for support on equipment for high-

speed measurement.

I would like to acknowledge Dr. Anthony Martinez, Dr. Yongchun Xin, and Dr. Hui

Su for numerous discussions and lectures on related topics that helped me improve my

knowledge in the area. I am also thankful to Nader Naderi, Li Wang and Chi Yang for

their help and collaboration on the measurements. I am also grateful to my fellow

graduate students in the group: Changyi Lin, Aaron Moscho, Mohamed El-Emawy,

Therese Saiz, and Furqan Chiragh.

Finally, I would like to express my heart-felt gratitude to my family. I appreciate my

parents for their continuous support and encouragement. I am also grateful to my wife,

Ye Zhou, for her understanding, support and love. None of this would have been possible

without them. .

TECHNIQUES FOR HIGH-SPEED DIRECT MODULATION

OF QUANTUM DOT LASERS

BY

YAN LI

ABSTRACT OF DISSERTATION

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

Optical Science and Engineering

The University of New Mexico Albuquerque, New Mexico

May, 2008

v

Techniques for High-Speed Direct Modulation of Quantum Dot Lasers

By

Yan Li

M.S. Optics, Sichuan University, 2000

Ph.D, Optical Science and Engineering, 2008

As a major component of optical transmitters, directly-modulated semiconductor

lasers are widely used in today’s fiber optical link systems by taking its advantage of their

low cost, compact size and low power consumption. In this work, techniques to improve

the high frequency modulation characteristics of semiconductor lasers with a

low-dimensional active region medium, specifically quantum dots (QDs), are studied.

These techniques include a p-doped active region in single-section QD lasers, the

gain-lever effect in two-section lasers and the injection-locking technique.

Firstly, the modulation performances of p-doped InAs/GaAs QD lasers were studied.

Contrary to the theoretical predictions, the modulation efficiency and the highest

relaxation frequency of 1.2-mm cavity length lasers decreasse monotonically with the

p-doping level from 0.54 GHz/mA1/2 and 5.3 GHz (un-doped dots), to 0.46 GHz/mA1/2

and 3.6 GHz (40 holes/dot). Although the maximum ground state gain of the p-doped

lasers is increases with p-type concentration, the undesired increase in internal losses

induces stronger gain saturation and gain compression, thus degrading the high-speed

performance. The degradation of the modulation performance of the p-doped device is

vi

also attributed to a higher gain compression factor due to the carrier heating effect..

Secondly, the gain-lever effect is studied in two-section QD lasers in order to

enhance the modulation efficiency and 3-dB bandwidth. An 8-dB modulation efficiency

enhancement is achieved using the p-doped QD laser. Due to the stronger gain

saturation with carrier density, it is found that un-doped QD devices show a more

significant gain-lever effect over p-doped devices. A 20 dB enhancement of the

modulation efficiency is demonstrated by the un-doped QD laser. A new modulation

response equation is derived under the high photon density approximation, and a 1.7X

3-dB bandwidth improvement is theoretically predicted by the new model and realized in

an un-doped QD gain-lever laser under extreme asymmetric pumping conditions. It is

also demonstrated for the first time that the 3-dB bandwidth in gain-lever laser can be 3X

higher than the relaxation frequency instead of 1.55X in typical single-section lasers.

Finally, injection locking in QDash lasers was analyzed. By varying the power

injection ratio and detuning, the modulation bandwidth of a 0.5-mm QDash Fabry-Perot

slave laser by 4 times. By analyzing the curve fitted data, it was observed that the

inverted gain-lever modulation response equation can approximate the injection-locking

system in the Period 1, non-linear regime. Based on the gain-lever model, an analytical

expression for the relaxation frequency of an injection-locked laser is derived, and the

maximum achievable 3-dB bandwidth is predicted and verified experimentally.

vii

TABLE OF CONTENTS

LIST OF FIGURES…………………………………………………………………….. x

LIST OF TABLES…………………………………………………………………….. xv

Chapter 1 Introduction……………………………………………………………….. 1

1.1 Analog fiber-optic link…………………………………………………………………….. 1

1.2. Optical transmitter……………………………………………………………………….. 4

1.3. Introduction to quantum dot or dash semiconductor lasers…………………………… 6

1.3.1 A Brief History of Quantum Dot Semiconductor Lasers……………………………… 6

1.3.2. Epitaxy and quantum dot formation………………………………………………….. . 8

1.3.3 Quantum Dot Advantages…………………………………………………………….. 10

1.4 Improving modulation performance of QD lasers…………………………………….. 13

1.4.1 p-doped QD lasers……………………………………………………………………. 13

1.4.2 Gain-lever effect……………………………………………………………………… 15

1.4.3 The injection-locked laser…………………………………………………………….. 16

1.5 Organization of dissertation…………………………………………………………….. 18

References……………………………………………………………………………………. 20

Chapter 2 Modulation Bandwidth of p-doped Single Section Quamtum Dot lasers 30

2.1. Introduction……………………………………………………………………………… 30

2.2. Modulation response equation for single section QD lasers………………………….. 32

2. 3 Wafer growth and device fabrication………………………………………………….. 36

2.4. Static performance of the un-doped and p-doped lasers……………………………… 36

2.5. Small signal modulation response of the 1.2 mm devices…………………………….. 40

2.6. Small signal modulation response of 0.8 mm HR coated devices…………………….. 47

viii

2.7. Summary………………………………………………………………………………. 49

References…………………………………………………………………………………….. 50

Chapter 3 Gain-lever quantum dot lasers……………………………………………. 54

3.1 Introduction……………………………………………………………………………… 54

3.2. Modulation characteristic of gain-lever QD lasers…………………………………… 56

3.2.1 Basic concept of the gain-lever effect………………………………………………... 56

3.2.2 Motivation for gain-lever QD lasers………………………………………………….. 58

3.3. Novel response model of gain-lever lasers…………………………………………….. 60

3.3.1 The rate equation of gain-lever lasers……………………………………………….... 60

3.3.2 Modulation efficiency enhancement………………………………………………….. 65

3.4 IM efficiency enhancement of p-doped gain-lever QD lasers………………………… 68

3.4.1 Wafer structure and device fabrication……………………………………………….. 68

3.4.2 Static characterization and gain measurement………………………………………... 71

3.4.3 Experiment setup for dynamic characterization of p-doped gain-lever QD laser..……76

3.4.4 Modulation efficiency enhancement………………………………………………….. 81

3.5 Relative modulation response equation………………………………………………… 83

3.6 Bandwidth enhancement in the gain-lever device……………………………………… 88

3.7 Un-doped gain-lever QD device…………………………………………………………. 90

3.7.1 Gain measurement using the segmented-contact method……….…………………….90

3.7.2 Wafer structure and device configuration…………………………………………….. 91

3.7.3 AM modulation for the un-doped QD gain-lever laser……………………………….. 95

3.7.4 Bandwidth enhancement in the un-doped device……………………………………. . 98

ix

3.8 Summary………………………………………………………………………………… 100

References…………………………………………………………………………………… 101

Chapter 4. Modulation Characteristics of Injection-locked Quantum Dash Lasers………………………………………………………………………………….. 103

4.1 Introduction……………………………………………………………………………... 103

4.2 Basic concept of injection-locking………………………………………………………104

4.2.1 Injection locking concept and history……………………………………………….. 104

4.2.2 Advantages of optical injection locking…………………………………………….. 105

4.3 Device description and experimental set up…………………………………………... 108

4.3.1 Wafer structure and device fabrication…………………………………………….... 108

4.3.2 Experimental setup………………………………………………………………….. 110

4.4 Bandwidth enhancement of injection locking QDash laser………………………….. 112

4.5 Injection-locking and the gain-lever…………………………………………………… 117

4.4.2 Bandwidth enhancement explanation using gain-lever equation…………………… 121

4.6 Summary………………………………………………………………………………… 126

References…………………………………………………………………………………… 127

Chapter 5 Conclusion and future work…………………………………………… 129

5.1 Summary……………………………………………………………………………….. 129

5.2 Suggestions for future work…………………………………………………………… 131

x

LIST OF FIGURES

Fig. 1.1 The schematic of basic components of a analog fiber-optic link. .................. 2

Fig. 1.2 Illustration of (a) direct and (b) external modulation of transmitter in

fiber-optic links .................................................................................................... 4

Figure 1.3 Self-assembly growth technique for InAs quantum dots by S-K mode ..... 9

Fig. 1.4 The density of states functions for bulk, quantum well, quantum wire, and

quantum dot active regions. ................................................................................11

Fig 2.1 Layer structure of the p-type quantum dot device with variable doping

density ................................................................................................................ 35

Fig. 2.2 The L-I curve of ridge waveguide lasers fabricated from p-doped and

un-doped QD wafters. ........................................................................................ 39

Fig 2.3 Signal-Ground configuration for Hi-speed testing. The adjacent metallic chip

moves the ground so that it is coplanar with the surface of laser anode contact.

............................................................................................................................ 41

Fig 2.4 Modulation response of 1.2 mm-long un-doped and p-doped QD RWG lasers.

The normalized current（I-Ith）is 8.5. .............................................................. 42

Fig. 2.5. Relaxation frequency versus the square root of the bias current above

threshold of 1.2 mm-long cavity length un-doped and p-doped lasers.............. 45

Fig. 2.6 Squared relaxation frequency versus output power for four lasers the set of QD

xi

lasers with different p-doping level. .................................................................. 46

Fig 2.7 Relaxation frequency versus the square root of the normalized bias current of

the three doped lasers with one HR-coated facet and cavity length of 800 μm. 48

Fig 3.1 Schematic of the two-section gain-lever semiconductor laser, with the

variation of modal gain versus carrier density. .................................................. 56

Fig 3.2 The typical optical gain versus current density relationship for QW and QD

materials. QW is logarithmic and the QD demonstrates exponential saturation.

............................................................................................................................ 59

Fig 3.3. The modulation response of a two-section gain-lever QD laser, with

curve-fitted data using a single section model. .................................................. 64

Fig 3.4 Calculated modulation efficiency enhancement vary with h for g =3, 5 and 10,

............................................................................................................................ 67

Fig 3.5. The layer structure of p-doped QD lasers (wafer #224) ............................... 69

Fig 3.6. The flow chart of the processing procedure for a two (multi)-section device.

............................................................................................................................ 70

Fig 3.7. The evolution of inverse differential efficiency with cavity length for p-doped

QD lasers. The internal loss and injection efficiency are calculated by curve

fitting the measured data.................................................................................... 72

Fig. 3.8 The calculated threshold modal gain as a function of threshold current density.

The data was curve-fitted using (a) the exponential gian model, (b) new

square-root gain model. ..................................................................................... 75

xii

. Fig 3.9 P-I curve of the gain-lever device under the uniformly biased condition ... 77

Fig 3.10 The lasing spectrum of the p-doped gain-lever RWG laser......................... 77

Fig 3.11 The high-speed testing set up for dynamic characterization of the p-doped

gain-lever laser. .................................................................................................. 78

Fig 3.12 Modulation response of the gain-lever laser under different uniformly bias

condition. ........................................................................................................... 80

Fig 3.13. The evolution of damping rate with relaxation frequency under different

uniformly bias conditions. ................................................................................. 80

Fig 3.14 Modulation efficiency enhancement of p-doped QD gain-lever lasers ....... 82

Fig 3.15. The modulation response of a two-section gain-lever QD laser, with fitted

curves using single-section and new two-section model ................................... 85

Fig 3.16 Normalized resonance frequency as a function of normalized gain in the

modulation section plotted based on the one-section model. ............................ 87

Fig 3.17 Normalized resonance frequency as a function of normalized gain in the

modulation section plotted based on the new two-section model...................... 87

Fig 3.18 The simulation of the modulation responses of a gain-lever QD laser which is

under extreme asymmetrically pumping............................................................ 89

Fig 3.20. Schematic of the segmented contact device. The long absorber is achieved by

wire-bonding multiple section together and used to minimize back reflection. 92

Fig. 3.21. Net modal gain spectra of a 10-stack undoped QD device........................ 94

Fig. 3.22 Dependence of the net modal gain on injected current density in the QD

xiii

device. ................................................................................................................ 94

Fig 3.23. L-I characteristics of two uniformly biased un-doped QD devices............ 95

Fig 3.24. The modulation responses for the uniform and asymmetrically pumped cases

in the un-doped QD laser. .................................................................................. 97

Fig 3.25 The modulation efficiency enhancement depends on normalized gain Ga0/G0

for different h value. .......................................................................................... 97

Fig 3.26 The modulation responses for device #1 biased asymmetrically and uniformly.

The power lever is 6.5 mW/facet. The ratio of 3-dB bandwidth of the

asymmetrically to uniformly pumping case is 1.3. ............................................ 99

Fig 3.27 The modulation responses for device #1 biased asymmetrically and uniformly.

The power level is 7.9 mW/facet. The ratio of 3-dB bandwidth of the

asymmetrically to uniformly pumping case is 1.7. ............................................ 99

Fig 4.1 The schematic of optical injection locking system...................................... 104

Fig 4.2 The spectra of the free running and the injection locked F-P laser ............. 107

Fig 4.3 The layer structure of the 5-stack InAs QDash laser designed for 1550 nm

operation. ......................................................................................................... 109

Fig 4.4 AFM image of the QDash layer................................................................... 109

Fig 4.5 Schematic of the injection locking experimental setup ................................111

Fig. 4.6. The modulation responses of the injection-locked laser at different injection

power levels. .....................................................................................................113

Fig. 4.7. The spectra of the free-running QDash Fabry-Perot and injection-locked laser

xiv

(upper), with the corresponding modulation responses of the injection-locked

laser locked at different side modes (lower). ....................................................114

Fig. 4.8 Modulation responses of the free-running FP laser and the injection-locked

laser under different detuning conditions..........................................................116

Fig 4.9 Simulated modulation responses of injection-locked lasers using Eqn (4.1), the

bandwidth incrased with γinj............................................................................. 124

Fig. 4.10 Variation of γinj as function of detuning.................................................... 125

Fig 5.1 The experimental setup for injection-locked QD lasers. The polarization status

is carefully controlled. . ................................................................................... 133

xv

LIST OF TABLES

Table 2.1. Static performance of un-doped and p-doped lasers ................................. 37

Table 2.2. Dynamic performance of the un-doped and p-doped lasers ..................... 40

Table 4.1 The curve fitting results for response curves at different detuning using Eqn

(4.6) and Eqn (4.1). .......................................................................................... 120

1

Chapter 1 Introduction

1.1 Analog fiber-optic link

Optical communication systems have been the mainstream information transmission

system in past decades and are still dominant today thanks to the invention and

development of broad band semiconductor lasers, low loss fibers, fast photodetectors and

other high quality optoelectronic components. The fiber-optic link has many advantages

which include tremendous available bandwidth ( ~200 THz), very low transmission loss

and immunity to electrical disturbance etc; all of this makes a fiber-optic link the

preferred transmission solution in many applications [1].

The digital fiber-optic link has a major role in present optical communication

systems. Fiber optic transmission of digital data for long haul and metro access is widely

used in the communication industry. Normally, in a digital transmission system, the signal

is sampled and digitized first, then the digital format signal is transmitted via a series of

optical pulses in which the high and low power levels represent either the number 1 or 0.

However, RF or microwave signals often need to be transmitted, distributed and

processed directly without going through the costly digital encoding process. The analog

optical transmission system aims to reproduce an identical version of the input signal at

the output. Since the original type of any signal is actually an analog signal, it is often

more cost efficient to transmit the data in its native format. Additionally, the analog

2

optical link offers more bandwidth efficiency and thus allows a higher data transmission

rate [2].

In Fig 1.1, a typical analog fiber-optic link diagram is shown, which is similar to a

traditional analog microwave transmission system in terms of the input and output ends.

It contains a modulated optical source at the sending end, which is modulated in an

analog manner. The optical fiber provides a transmission medium in which the modulated

optical signals can be transmitted and distributed. These modulated optical signals are

detected and demodulated at the receiving end to recover the RF signals.

One important application of the analog optical link technique is in commercial

communication systems such as cable-TV video distribution [3]. Older cable TV system

use a long cascade of electronic amplifiers that result in noise build-up and poor reception

near the fringes of the system coverage. Since the optical loss for fibers is very low,

analog fiber-optic links can provide the low cost network for distribution of RF signals to

Fig. 1.1 The schematic of basic components of a analog fiber-optic link.

Optical-to-RF demodulation device

RF Input

Fiber RF-to-Optical modulation device

Fiber-Optic link

RF output

3

end users by decreasing the number of electronic repeaters. An RF signal is directly

distributed from a system head to local neighborhoods via a star configuration of fiber

optic cables. Then the signal is converted back to analog electronics over a conventional

coaxial cable and delivered to end subscribers.

In the high frequency regime, an analog fiber-optic link offers an attractive

alternative to electrical systems too. The traditional microwave and millimeter wave

transmission systems, using coaxial cables and metallic waveguides, have extremely

large attenuation and consequently, are complex and expensive. Conversely optical fibers

have a small size, low weight, and more importantly, are immune to electromagnetic

interference such as lighting and electrical charges. Applications of analog optical links

include the up-link cellular remote antenna and phased array radar system [4]. By using

fiber as a transmission waveguide, both the design of new sites, and physical expansion

of the network are much easier. This technique, also referred as fiber-to-the-antenna

(FTTA) is employed by the wireless communication company to replace the coaxial

cable between the radio base station (RBS) and the antenna. Additionally, an available

200 THz bandwidth of optical fiber also offers an advantage. It is easy to mix traffic in

the same fiber by allocating different sub-carriers to different traffic. The analog video

signal and data transmission can all be carried on the same fiber. A dense wavelength

division multiplexed (DWDM) analog fiber-optic system was demonstrated that

distributes RF over fiber up to 3 GHz. This system can provide new services such as PCS,

broad band wireless internet and digital video [5].

4

1.2 Optical transmitter

The optical transmitter is one of the most researched subjects in fiber optical

communications. To enhance the transmission capability of a fiber-optic link, a high

performance optical source or transmitter is required. The characteristics of the

transmitter often determine the maximum length of a fiber link and the data rate that is

achievable. The main component of a transmitter is a semiconductor diode laser ( LD). In

present fiber-optic link systems, the typical operation wavelength of the semiconductor

laser is 1310 nm and 1550 nm, which correspond to the dispersion and absorption

minimum of optical fibers, respectively. The RF (10KHz-300MHz) and microwave (300

MHz to 300 GHz) signals can be modulated on to the laser. Analog modulation optical

Fig. 1.2 Illustration of (a) direct and (b) external modulation of transmitter in fiber-optic links

CW laser

Bias-T

DC

RF

Direct modulation

CW Laser

DC

External Modulator

External modulation

RF

5

transmitters can be achieved either by using an external modulator or by direct

modulation of the semiconductor laser [6]. In Fig 1.2, the diagram of direct and external

modulation in a fiber-optic link is shown.

Direct modulation can be realized by directly varying the laser drive current with the

information signal to produce a varying optical output power. The system is relatively

simple and low cost. When using a directly modulated laser diode for a high-speed

transmission system, the modulation frequency can not be larger than the relaxation

frequency of the laser, which is a function of both the stimulated lifetime and the photon

lifetime. Moreover, analog modulation of a laser diodes is carried out by making the

drive current above threshold proportional to the information signal, so a linear relation

between the light output and the current input is required, but this linear relation cannot

be achieved in semiconductor lasers. The intrinsic non-linear coupling between an

electron and photon of semiconductor lasers results in undesired signal degradation.

Another limitation on direct modulation laser diodes is the electron-photon conversion

efficiency [7]. Typical values for end-to-end RF loss are in the range of -20 dB to -30 dB

due principally to the efficiency of RF-light conversion. An electrical amplifier is usually

used to compensate for loss and boost the signal-to-noise ratio for weak signals.

The limitations of direct modulation described above can be overcome by external

modulation. The external modulator, which can either be a separate device or an integral

part of the package, has high linearity, high optical power, low chirp and low noise.

However, it also suffers from high cost and power consumption. In this work, We will

6

focus on improving the modulation bandwidth and efficiency of directly modulated low

dimensional confined semiconductor lasers, called quantum dot (QD) lasers. In the next

section, the development and current status of QDs will be reviewed first.

1.3 Introduction to quantum dot or dash semiconductor lasers

1.3.1 A Brief History of Quantum Dot Semiconductor Lasers

The first successful semiconductor lasers with GaAs and GaAsP alloys were

demonstrated by several groups in 1962 [8, 9]. These lasers were homostructure devices

that had no any carrier confinement mechanism and could only be operated under pulse

conditions and very low temperature. With the development of new growth and

processing techniques, the performance of semiconductor laser has been improved

significantly over the past forty years. In one of the revolutionary steps, heterostructure

lasers were demonstrated by Alferov and Hayashiand et. al in the late 60s and 70s [10, 11,

12, 13]. The threshold current density was dramatically reduced from more than 104

A/cm2 to the order of 102~103 A/cm2 by applying a layer of one semiconductor material

( active layer) sandwiched between two layers of another material that has a wider band

gap. The large-scale commercial application of laser diodes became possible since then.

As the thickness of active layer drops below 10 nm, the distribution of available

energy states for electrons and holes confined in the active layer changes from

quasi-continuous to discrete. This is the so called quantum effect. The idea that the

quantum effect could be used in semiconductor lasers was first suggested by Henry and

7

Dingle in early 1975 [14]. It wasn’t until the late 1970s and early 1980s that Dupuis and

Tsang et. al. demonstrated the earliest quantum well (QW) lasers grown by metal-organic

chemical vapor deposition ( MOCVD) and molecular-beam epitaxy (MBE) techniques,

respectively [15, 16]. Over the past twenty years, QW lasers have been fully developed

with further threshold current reduction and larger power range coverage. Quantum size

effect also can be used to change the energy gap in order to cover a wider wavelength

range (from visible to IR) by varying III-V alloy composition and QW thickness. [17, 18,

19]. The success of QW lasers inspired more efforts to explore semiconductor materials

with multi-dimensional carrier confinement. Quantum dots (QD) are the semiconductor

nanostructures that act as artificial atoms by confining electrons and holes in three

dimensions. Arakawa and Asada et. al [20, 21] predicted in the early 1980s that QD

lasers should exhibit performance that is less temperature-dependent and has less

threshold current density than existing semiconductor lasers. These theoretical models

were based on lattice-matched heterostructures and an equilibrium carrier distribution.

However, the challenge in realizing quantum dot lasers with superior operation to that

shown by quantum well lasers is that of forming high quality, uniform quantum dots in

the active layer. Initially, the most widely followed approach to forming quantum dots

was through electron beam lithography of suitably small featured patterns (~300 Å) and

subsequent dry-etch transfer of dots into the substrate material. The problem that plagued

these quantum dot arrays was their exceedingly low optical efficiency: high

surface-to-volume ratios of these nanostructures and associated high surface

8

recombination rates, together with damage introduced during the fabrication itself,

precluded the successful formation of a quantum dot laser. The best quantum-box laser,

developed with lattice-matched heterostructures, demonstrated laser operation with an

unpractical threshold current density of 7.5 kA cm2 in pulsed operation at a low

temperature of only 77K [22]. At the beginning of the 1990s, it was realized that the

strain relaxation on step or facet edges may result in the formation of high density and

ordered arrays of quantum dots for lattice-mismatched materials [23, 24, 25]. The first

self-assembled QD laser was demonstrated in 1994, with fully quantized energy levels in

both bands and a strongly inhomogeneous broadened gain spectrum [26]. Since then the

field has seen steady progress, the performance of self-assembled QD lasers have now

reached or surpassed those of the well-established quantum-well lasers. [27, 28, 29]

1.3.2. Epitaxy and quantum dot formation

Self-assembled QD growth is realized from lattice mismatched combinations of

semiconductor materials and the most common mode used for growth is the

Stranski-Krastanow (S-K) mode. If the deposited semiconductor is slightly mismatched

to the substrate, the deposited film will be strained, so that its in-plane lattice constant fits

the lattice constant of the substrate. Growth will continue pseudomorphically until the

accumulated elastic strain energy is high enough to form dislocations. In S-K mode, the

growth of a pseudomorphic 2D layer is followed by reorganization of the surface material

in which 3D islands are formed. Fig 1.3 is an illustration of 2-D wetting layer and 3-D

9

island formation in S-K mode that is responsible for forming the InAs QDs on a GaAs

substrate.

Figure 1.3 Self-assembly growth technique for InAs quantum dots by S-K mode

GaAs substrate

InAs Deposition

Wetting layer ~ 1.0 monolayer

GaAs substrate

InAs Deposition

GaAs substrate

InAs Deposition

Wetting layer ~ 1.0 monolayer

GaAs substrateDot nucleation ~1.5 monolayer

GaAs substrateGaAs substrateDot nucleation ~1.5 monolayer

15-20 nm

50-100 nm spacing

Fully formed dots ~2.0-2.5 monolayer

GaAs substrate

15-20 nm

50-100 nm spacing

Fully formed dots ~2.0-2.5 monolayer

GaAs substrate

10

1.3.3 Quantum Dot Advantages

Due to the three dimensional confinement of the carriers in QDs with dimensions

comparable to or below the exciton’s Bohr radius, the density of states consists of a series

of atomic-like delta functions, which lays the foundation upon which many QD

advantages are built. Fig. 1.4 illustrates the density of states functions for bulk, quantum

well, quantum wire, and quantum dot active regions. For QDs, the state density is a

δ-function in energy, which is dramatically different from either bulk (continuous) or QW

(step function). For the real QD materials, the density of states has a line broadening

caused by fluctuations in the quantum dot sizes. The fundamental advantages of QD

lasers include an ultra-low threshold current, temperature-insensitive operation, high

material gain and differential gain, a decreased linewidth enhancement factor, an

ultra-broad bandwidth, easily saturated gain and absorption, and a larger tuning range of

the lasing wavelength.

Ultra-low threshold current A reduction in the threshold current density can be

attributed to the small scaling of the active region and reduced density of states. There is

less material to populate with electron-hole pairs in order to establish population

inversion. Also the atom-like density of states function leads to lower transparency

current because the number of noncontributing lower energy states that need to be filled

is further reduced [30, 31]. In 1999, Liu et. al demonstrated the QD laser with threshold

current density of 26 A/cm2 using a dots-in-a-well (DWELL) structure [32]. The

11

threshold current density below 20A/cm2 is demonstrated by Park et. al. [33].

Fig. 1.4 The density of states functions for bulk, quantum well, quantum wire, and quantum dot active regions.

Bulk QW

QWire QD

2/1~ EdEdN .~ ConstdEdN

2/1~ −EdEdN )(~ EdEdN δBulk QW

QWire QD

2/1~ EdEdN .~ ConstdEdN

2/1~ −EdEdN )(~ EdEdN δ

12

Temperature insensitive threshold, high T0 Due to their well separated energy

levels, the QD laser is expected to be operated with high characteristic temperature T0.

However, this has been achieved only in narrow temperature ranges and typically below

room temperature [26, 34]. The P-type doping technique in the QD active region was

proposed by Shchekin and Deppe to compensate the closely spaced hole levels. Using

this approach, an InAs/GaAs QD laser in the 1310 nm range with 213 K T0 and an

InAs/InP 1500 nm QD laser with 210 K T0 have been reported [35, 36] separately. A

value of T0=363K at room temperature is realized by tunnel injection QD lasers at a

wavelength of 980 nm [37].

Small linewidth enhancement factor The symmetry inherent in the QD density of

states function is manifested by the symmetry in the gain spectrum, which is important

because it predicts that the zero dispersion point of refractive index aligns with the gain

peak. The resulting benefit is that the linewidth enhancement factor (LEF), which is a key

parameter in the characterization of semiconductor lasers, is predicted to be zero, leading

to chirp-free operation. The common ways used to measure LEF are based on the

analysis of the amplified spontaneous emission (ASE) [38], on the FM/AM response ratio

under small signal current modulation [39] and pump-probe experiments [40]. The

published value of LEF can vary a significant amount depending on which measurement

techniques are used. Experiments have reported a great variety of values for the LEF

ranging from 0 to 50 [38, 41-43].

Easily saturated gain and absorption Due to the limited number of available

13

states, the gain of QD lasers is easily saturated by increasing the number of injected

carriers. These characteristics result in QDs being an ideal material system for

mode-locked lasers (MLL) and super-luminescent light emitting diodes (SLEDs) [44 ,45].

The strong gain saturation with carrier density is also the main motivation to explore

gain-lever effect using QD materials, which will be discussed in Chapter 3.

1.4 Improving modulation performance of QD lasers

1.4.1 p-doped QD lasers

The QD lasers have generally been demonstrated with the performance over or matching

those of QW devices. However, there has always been some theoretical question about

the ultimate high-speed performance of direct-modulation QD lasers. First, the

inhomogenous linewidth, associated with an approximately 10% inhomogeneity in size

and fluctuation in shape and composition broadening, severely limits the performance of

QD lasers. Second, the capture/relaxation time of carriers in QD’s is predicted to be much

longer than in QW’s because of the “phonon bottleneck” effect. The excited and ground

states are not typically separated by phonon energies, thus only multi-phonon assisted

relaxation events are permitted, which are typically much slower [46]. Even though some

fast mechanisms were proposed, such as electron-hole scattering [47] and Auger process

[48], and it has been proven that the “phonon bottleneck” effect is not significant at room

temperature and high current bias condition, 1 – 10 ps phonon-scattering relaxation time

14

still hinders the high-speed modulation of QD lasers. The third limitation is contributed to

the so called “hot carrier” effect. In the self-assembled QDs grown by S-K mode, the

number of wetting layer/barrier states is much larger than the number of available dot

states, thus the injected electrons predominantly reside in the wetting layer and barrier

states. The relaxation process from the 2-D wetting layer states to the lasing state in QDs

is very slow [49]. The reduction of the electron-hole scattering rate and wetting layer

carrier occupation leads to severe gain saturation and limits the achievable modulation

bandwidth of QD lasers. Two techniques have been proposed to overcome the hot carrier

effect: tunneling injection (TI) [50] and p-doping in the QD active medium [51].In the

tunneling injection scheme, “cold” electrons are injected into the ground state of the QD

by direct or phonon-assisted tunneling from an adjacent QW layer. Since the injection

rate is comparable with the stimulated recombination rate, a quasi-Fermi distribution of

carriers can be maintained. The p-doping technique is based on the theory that the hole

levels are closely spaced in energy so that there is a thermal broadening of the hole’s

distribution amongst the many available states. This thermal broadening results in the

depletion of the ground state hole distribution at elevated temperatures. The p-doped

layer act as a supplier of extra holes, thus, the hole population in the ground state is

compensated with fewer injected electron-hole pairs from the electrical contact. However,

even though a slight bandwidth enhancement is reported by p-doped QD lasers over the

un-doped conventional QD lasers [52], the prediction has not yet been shown as pointed

out in Ref [49].

15

1.4.2 Gain-lever effect

As we discussed in section 1, one of the limitations of directly-modulated lasers in

analog fiber optic links is low efficiency of the electron-photon conversion. The typical

values for end-to-end RF loss are in the range -20 dB to -30 dB, which means much

higher microwave power is required for full optical modulation [53, 54]. An additional

electrical amplifier may be needed for signal boost, and system cost will increase as well.

Therefore, improving modulation efficiency of lasers is a key to reducing the link loss in

fiber-optic systems. The two-section laser based on the gain-lever effect was proposed in

the late 1980s to accomplish high modulation efficiency in intensity modulation (IM) and

frequency modulation (FM), and even broad wavelength tunability [54-56]. The

gain-lever effect is based on the sublinear relationship between gain and carrier density in

semiconductor lasers. A gain lever laser consists of two electrically isolated sections,

which are biased asymmetrically. One section is biased at a low gain level and is RF

modulated. Another section is biased at a high gain level. When the device is biased

above threshold, the sum of the gain of two sections is clamped at a constant value. If one

section increases in optical gain by increasing the bias, the gain of the other section must

be decreased to keep the total gain of two sections constant. Correspondingly, the

differential gains of the two sections are different under this asymmetrically biased

condition. In the normal gain lever case, since the modulation efficiency enhancement is

proportional to the ratio of the differential gains of the two sections, the operation point

16

should be chosen where the differential gain of the modulation section is larger than that

of gain section. The idea of the gain lever effect was first proposed by Vahala et. al. in

1989 [57]. Subsequently, the gain-lever effect was applied to both the ridge waveguide

and distributed feedback (DFB) QW lasers. A 22 dB modulation efficiency enhancement

was demonstrated by Moore and Lau using an electrically-pumped two-section QW laser

[54]. By interchanging the bias points of the two sections of the gain-lever laser, the

inverted gain-lever laser showed 22 GHz/mA FM efficiency [55]. The gain-lever effect

also can be used in DFB lasers to improve the tuning behavior and obtain better control

of the power-current relations [58]. However, the existing literature only explored QW

gain-lever devices and lacks discussion on the possibility of bandwidth enhancement

using the gain-lever laser. Due to the delta-function like density of states, QD lasers,

which have stronger gain saturation characteristic and larger differential gain, are

expected to demonstrate a bigger gain-lever effect. The modulation efficiency and

bandwidth enhancement brought by gain-lever QD lasers will be presented in this work.

1.4.3 The injection-locked laser

For analog fiber-optic transmissions, the application of injection-locked lasers has

been demonstrated in radio-over-fiber [59], mm-wave generation [60] and optical

switching [61]. An optical injection-locking system consists of two sources, which are

usually called a master and slave laser. The output light from the master laser, which is

17

typically a narrow linewidth DFB laser, is injected into the slave laser. When the optical

frequencies of the two lasers are close enough, the phase locking phenomenon can occur.

The CW operation behavior and modulation characteristic of the slave laser can be

significantly changed such as reduced linewidth, enhanced relaxation frequency and

modulation bandwidth, suppressed mode hopping, reduced chirp and relative intensity

noise. The research on injection-locking between two semiconductor lasers was launched

by Kobayashi et al. in the early 1980s [62]. Since then, many advantages of

injection-locked lasers have been demonstrated including modulation bandwidth

enhancement, chirp reduction, nonlinear distortion reduction, and relative intensity noise

reduction [63-66]. The 2.7X bandwidth enhancement was reported using a 1550 nm

VCSEL as a slave laser [65]. Jin et. al demonstrated bandwidth enhancement on

injection-locked Fabry-Perot (F-P) QW lasers [66].

In this work, the analog modulation characteristics of injection-locked quantum dash

lasers are discussed for the first time. It is realized that both the gain-lever and injection

locking lasers are actually a coupled oscillator system and share the same frequency

response function under certain assumptions. A clearer physical view of the modulation

characteristics of the injection-locked laser is provided, which has been blurred

previously by a complicated set of fitting parameters in the frequency response function.

18

1.5 Organization of dissertation

This dissertation describes the direct modulation characteristics of single and

two-section QD lasers and injection-locked quantum dash lasers.

Chapter 2 discusses the static performance and modulation frequency response of

un-doped and p-doped InAs/GaAs QD lasers with different doping levels. It is shown that

p-doping in the QD active region increases not only the ground state gain, but also the

internal loss. The undesired increase in internal losses induces gain saturation and gain

compression, thus degrading the high-speed performance of p-doped QD lasers. We

found that the modulation bandwidth and relaxation frequency decrease monotonically

with the p-doping level.

In chapter 3, the modulation response of gain-lever quantum dot lasers will be

studied. The modulation efficiency enhancement, which is desired for analog fiber optic

links, was achieved by taking advantage of the gain-lever effect in both p-doped and

un-doped QD lasers with a two-section configuration. Due to the stronger gain saturation,

the un-doped device shows a higher gain-lever effect over the p-doped device. The new

relative response function was derived under the high photon density approximation. A

1.7X 3-dB bandwidth improvement is theoretically predicted by the new model and

realized in un-doped QD gain-lever laser. It is also demonstrated for the first time that

in gain-lever lasers, the 3-dB bandwidth can be 3X higher than the relaxation frequency

instead of 1.55X in typical single section lasers.

19

Chapter 4 describes the modulation characteristics of injection-locked F-P quantum

dash lasers. The bandwidth enhancement is observed by varying the injection power and

changing the detuning. It is found that the side mode locking variation has no significant

impact on modulation response so that the power injection ratio should refer to the total

slave power, not the individual modes. The new finding in this chapter is a new equation

to describe the modulation response of the injection-locked laser, which is inspired by the

gain lever model under high photon density approximation. The two key parameters for

injection-locked laser: the frequency detuning and injection power ratio are included in a

single parameter in the gain-lever model which represents the effective damping rate of

the master laser. The analytical expression of the relaxation frequency is derived too. The

maximum achievable 3-dB bandwidth at a certain power level is predicted for the first time.

20

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30

Chapter 2 Modulation Bandwidth of p-doped Single Section

Quamtum Dot lasers

2.1. Introduction

Self-assembled quantum dot (QD) semiconductor lasers have been considered as a

potential candidate for high-speed devices due to their unique three-dimensional carrier

confinement [1, 2]. In planar quantum well materials, the density of state is a step-wise

continuous function. The electron and holes occupy a wide range of energy levels. Since

the lasing spectrum is relative narrow, the probability is small for the electron and holes

to occupy those states that couple to lasing mode. In contrast, for quantum dot materials,

which have a delta-function-like density of states, the spontaneous emission linewidth

and the gain spectra are theoretically much narrower, so the QD lasers can achieve very

high differential gain, which is one of the key parameters for creating high-speed

semiconductor lasers.

However, the conventional separate confinement heterostructure (SCH) InAs and

InGaAs QD lasers have not shown significant modulation bandwidth enhancement yet [3,

4]. The first factor that limits the modulation performance of QD lasers is inhomogeneous

linewidth broadening, stemming from the stochastic size distribution of the

self-assembled dots. The linewidth of photoluminescence is one of indicator of

uniformity of the dot’s size. The narrowest photoluminescence reported to date is 19 meV

31

[5], which is considerably wider than the linewidth limit of 5-8 meV due to homogeneous

lifetime broadening [6]. A larger variation in dot size results in lower peak modal gain as

well as differential gain in real QD lasers. The second limitation comes from the large

density of states of the wetting layer and barriers [6, 7]. In the Stranski–Krastanow

growth mode, a self-assembled QD layer is formed on top of a wetting layer. The

accessible states in the wetting layer can be as much as two orders magnitude greater than

that in the QDs. The injected carriers will predominately occupy the states in the wetting

layer, where the energy of the state is high. The relaxation time for those carriers from the

upper energy state to the lasing state is longer. This “hot carrier” effect influences the

performance of QD lasers by increasing the threshold current density, compressing the

gain and damping the frequency response. As result, the modulation bandwidth of

conventional SCH QD lasers is limited to about 6-7 GHz at room temperature. [3].

Two promising techniques have been demonstrated to solve the hot carrier effect

discussed above: Tunneling injection (TI) and p-doping of dots. Bhattacharya et al. [8]

proposed the tunnel injection technique in QD lasers by applying a QW layer adjacent to

a QD layer as an injector well. The “cold” carriers were injected into QD ground state by

direct or phonon-assistant tunneling process, then removed at relatively the same rate by

stimulated emission, so the carrier distribution will be maintained close to a quasi-Fermi

distribution and carrier hot-carrier effect can be by-passed. A 23 GHz 3-dB bandwidth

was achieved for 980 nm TI-QD lasers [8].

The P-doping technique in the QD active region was proposed by Shchekin and

32

Deppe to compensate the closely spaced hole level [7]. The extra holes avoid the gain

saturation with carrier density so that the maximum ground state gain and differential

gain is increased. The characteristic temperature and modulation bandwidth of QD lasers

can be improved significantly by p-doping. A T0 as high as 210 K was demonstrated in

the InAs/InP 1500 nm QD lasers [9] and 213 K for InAs/GaAs QD lasers in the 1310 nm

range was reported by Shchekin et. al [10]. A modulation bandwidth of 30 GHz was

theoretically predicted using a p-doped QD device [11]. Sugawara [12] et. al.

demonstrated a temperature-insensitive 10 Gb/ s operation within 20–70 °C using a

10-layer stack p-type QD active region that had a direct modulation bandwidth of 7.7

GHz at room temperature. Fathpour et al. [13] reported a 3 dB bandwidth of 8 GHz for a

p-doped device at 1.3 μm under pulse conditions, but compared with the un-doped QD

device the bandwidth enhancement is only few GHz in the p-doped device. Therefore, at

the experimental level, the prediction has not yet been shown as pointed out in Ref [11].

Besides, the studies on literature were limited on p-doped materials with low dot density,

and the gain enhancement has been achieved by p-doping at low dot density. But more

interesting case is high dot density QDs with high-doping level. This is the main topic of

this chapter.

2.2. Modulation response equation for single section QD lasers

Modulation response is the measure of any system response at the output to a signal of

33

varying frequency at its input. The carrier relaxation and spectral hole burning have a

greater influence on the dynamic property of QD lasers. In QD lasers, the discrete energy

does benefit the linewidth and differential gain, but it slows down the carrier relaxation

process. Different approaches have been proposed to investigate carrier dynamics in QD

lasers. [15-17]. In our dots-in-a-well (DWELL) SCH structure, the intraband relaxation is

assumed fast enough so that quasi-equilibrium can be kept. The slower relaxation process

such as carrier transport from the QW into the QD’s state can be treated as a parasitic RC

time constant. According to this simplification, a set of three rate equations model, which

was derived initially for QW lasers, can be applied to describe the small-signal

modulation response of QD lasers [4, 18]:

e

W

c

B

s

BB NNNedJ

dtdN

τττ+−−= (2.1a)

SSNGvNNN

dtdN g

s

W

e

W

c

BW

ετττ +−−−=

1)(

(2.1b)

p

g SS

SNGvdtdS

τε−

+

Γ=

1)(

(2.1c)

where NB and NW are the carrier density in the quantum well confined region and barrier

respectively, τs is the carrier recombination lifetime, τp is the photon lifetime, Γ is the

optical confinement factor, vg is the group velocity, G is the material gain that is a

function of carrier density, S is the photon density, ε is the non-linear gain compression

coefficient, τe is the active region escape time and τc is the carrier transport time, which

34

includes the capture time and various parasitic effects, such as the equivalent RC

constants of the packaging, since they are indistinguishable from the transport effect in

the experimental measurement. The small signal analysis gives the relative modulation

response as:

⎥⎦⎤

⎢⎣⎡ +−+

∝=2222

4

22

)2

()()2(11

)0()0(

)()(

)(fff

ff

is

fifs

fMr

r

c

πγτπ (2.2)

Where s is the photon density, i is injected current density, fr is relaxation frequency, γ is

the damping rate. The low-pass filter term arising from τc produces a low frequency

roll-off in the response curve. The relationship between fr and γ defines the so called K

factor as:

eff

2r

1τ

γ += Kf (2.3)

And

)1(4

(2

02

SSgV

fp

gr ετπ

χ+

)= (2.4)

satPP

GS

GG

+≡

+=

1100

ε (2.5)

where τeff is the effective carrier lifetime, a0 is the differential gain without gain

compression, and χ = 1+τe/τc is the modification factor due to the carrier transport with τe

the carrier escape time. The gain compression coefficient, ε, can be calculated using Eqn.

35

(2.4) if fr and S can be experimentally obtained. P is the output power measured at the

facet of the device. The introduction of Psat is for convenience to estimate at what output

power the gain compression becomes significant.

Fig 2.1 Layer structure of the p-type quantum dot device with variable doping density

Graded Al0.66->0Ga0.34->1As, p doped 2×1019 cm-3, 40 mm

Al0.66Ga0.34As Clading, p-doped, 3×1017 -5×1018 cm-3, 1300 nm

Graded Al0->0.66Ga1->0.34As, Un-doped 10 nm

GaAs, Un-doped 5 nm

GaAs, Un-doped 5 nm

GaAs, P-doped 5 nm

GaAs, Un-doped 5 nm

InAs/InGaAs, Undoped 7.8 nm , DWELL

Graded Al0.66->0Ga0.34->1As, Un-doped 10 nm

Al0.66Ga0.34As Clading, n-doped, 3×1017 -3×1018 cm-3, 1300 nm

Graded Al0.66->0Ga0.34->1As, n doped 3×1018 cm-3, 40 nm

n-GaAs substrate

n-GaAs buffer layer, -doped 5×1018 cm-3， 300 nm

p+-GaAs contact layer, p doped 3×1019 cm-3, 60 nm

GaAs, Un-doped 5 nm

6X

36

2. 3 Wafer growth and device fabrication

To compare the improvement of the p-doping technique, one un-doped QD wafer (# 632)

and three p-doped QD wafers with different doping level: 20 holes/QD (619), 30

holes/QD (618) and 40 holes/QD (620) were grown during the same campaign. The 1.22

μm InAs/InGaAs DWELL laser structure, which is shown in Fig. 2.1 was grown on an

n+-doped GaAs substrate. The active region consists of 6 DWELL stacks of self assembled

InAs QDs in a 7.8-nm wide, compressively strained InGaAs quantum well (QW) separated

by 15 nm GaAs barriers. The dot density is 2.5×1011 cm-2 for all four wafer samples. For

the p-doped wafer, there is a δ-doped layer added in the barrier 5 nm above each QW with

different sheet densities of beryllium. The total GaAs/InGaAs waveguide thickness is

about 137 nm. The cladding layer on the p-side is 1300-nm thick p-doped Al0.66Ga0.34As.

The cladding on the n-side is 1300-nm thick n-doped Al0.66Ga0.34As. The laser structure has

been capped with a 60-nm thick heavily p-doped GaAs layer.

2.4. Static performance of the un-doped and p-doped lasers

To examine the static operating parameters of un-doped and p-doped lasers, 50-um-wide

broad area lasers were fabricated out of these wafers. The samples were cleaved to

different cavity lengths ranging from 0.5-mm to 2-mm. The cavity-dependent

light-current (L-I ) characteristics were measured under pulse conditions (500-ns pulse

37

width and 1% duty cycle). The internal loss and injection efficiency can be derived from

the plot of the inverse of external quantum efficiency versus cavity length. The results are

listed in Table 2.1. It is well known that p-type doping can increase the maximum gain,

Gmax, of the QD laser as shown in the third column of Table 2.1. But the p-doped devices

have larger internal losses compared to the un-doped lasers, due to free-carrier absorption

and the internal loss increases with doping level. The injection efficiency does not

experience much change between un-doped and p-doped devices, because the diode laser

structure is same for these devices.

Table 2.1. Static performance of un-doped and p-doped lasers

Broad area lasers 1.2mm long RWGs Wafer # αi ηi Gmax Gth ith SE T0

un-doped 2 65 15 12 8 0.54 57 20 h/dot 7.5 56 22 17.5 25 0.36 48 30 h/dot 8.7 63 24 18.7 31 0.28 48 40 h/dot 10 60 25 20 32 0.32 32

The 3.5-μm-wide ridge waveguide (RWG) lasers were then fabricated from these

wafers to perform dynamic characterization. First, the sample was dry-etched to form

3.5-μm wide ridges using a BCl3 inductively-coupled plasma (ICP) etch. Then BCB

dielectric processing was applied for planarization and to isolate the p-type metal and the

etched upper cladding layer. The p-type metal is Ti/Pt/Au with a thickness of

50nm/50nm/250nm. After lapping and polishing of the substrate, Au/Ge/Ni/Au n-type

metallization was deposited, and the sample was annealed at 380°C for 1 minute. This

38

temperature is lower than the optimal value for annealing the time contact but is

necessary to avoid delamination of the BCB material from the ridge waveguide. Finally,

the sample was cleaved to 1.2-mm long laser diode bars for further testing.

The static performance measurements for RWG lasers were performed too under

pulsed conditions of 0.5 us and 1% duty cycle. The L-I characteristics for four devices are

plotted in Fig. 2.2. The slope efficiency (SE), the threshold modal gain and threshold

current density (at 200C) were extracted from the data in this figure and are listed in Table

1. The slope efficiency of the un-doped laser is larger than those of the p-doped lasers.

This can be attributed to the larger internal loss for p-doped material. For the lowest hole

concentration device, the value of SE is 0.36 W/A, which is similar to the value reported

by Fathpour et.al.[12]. This indicates our p-doped QD material is of high quality.

Generally, as the doping level increases, the slope efficiency goes down. A slightly lower

SE value in device 618 is due to the 10% measurement accuracy. The characteristic

temperatures, which are included in Table.1, are extracted by measuring the threshold

current from 200C-800C under CW operation. The value of 57 K is fairly typical for

un-doped QD devices with same structure. All p-doped lasers show lower T0 compared to

the un-doped laser. The lowest T0 occurs when the doping level is highest. This trend is

contrary to most previous reports that p-doped devices have higher T0 value [9, 10].

Large internal loss and non-linear gain compression arising from the heavy doping could

be contributing to this unusual behavior, more detailed discussions are presented in the

following part of this chapter.

39

Fig. 2.2 The L-I curve of ridge waveguide lasers fabricated from p-doped and un-doped

QD wafters.

40

2.5. Small signal modulation response of the 1.2 mm devices.

To prepare for high-speed testing, each RWG device was soldered using indium on a

Au-coated copper heat-sink and an “on-wafer” RF probe was used. As shown in Fig 2.3,

the signal-ground configuration was achieved by mounting another chip adjacent to the

device with the same thickness to minimize the parasitic capacitance and inductance. DC

and small-signal microwave signals were provided from port 1 of an HP8722D vector

network analyzer. The output of the laser diode was coupled into a tapered fiber ( the

coupling efficiency is about 10%) then collected by a Newport high-speed photodetector

(40 GHz bandwidth )，which was connected to port 2 of the HP8722D. The

measurements were performed on the four lasers by using the same RF calibration to

ensure consistency. The modulation response from each device is shown in Fig. 2.4.

Because of a low frequency roll-off in the detector response, the frequency range of study

covers from 700 MHz to 20 GHz. Based on Eqn [2.2-2.4], the modulation characteristic

parameters, such as relaxation frequency, fr and the K factor were extracted from Fig. 2.4

and are summarized in Table 2.

Table 2.2. Dynamic performance of the un-doped and p-doped lasers

Wafer max fr mod. eff. f-3 dB K-factor Psat

Unit GHz GHz/mA1/2 GHz ns mW

undoped 5.3 0.54 5.2 1.42 90

20 h/dot 4.6 0.51 4.6 1.14 62.7

30 h/dot 3.8 0.48 4.2 1.04 53.2

40 h/dot 3.6 0.46 4.4 1.01 18.4

41

Fig 2.3 Signal-Ground configuration for Hi-speed testing. The adjacent metallic chip moves the ground so that it is coplanar with the surface of laser anode contact.

S G

From Port 1 of 8722D

42

Fig 2.4 Modulation response of 1.2 mm-long un-doped and p-doped QD RWG lasers.

The normalized current（I-Ith）1/2 is 8.5.

43

The relaxation frequency, fr, versus the square-root of the current above threshold

( I-Ith)1/2 is plotted in Fig. 2.5 for the four different lasers. The maximum relaxation

frequency obtained at a normalized bias current of 10 decreases monotonically with the

p-doping level from 5.3 GHz (un-doped) to 3.6 GHz (40 h/dot). In the low bias range, the

fr increases linearly with root normalized current as expected. The relaxation frequency is

saturated when the root normalized current exceeds 7. From Fig. 2.2, it is confirmed that

heating effect can be neglected in our measurement since there is no roll off in the L-I

curves until about 140 mA. The ground state lasing is also confirmed across the whole

current range. This trend in fr arises from gain compression factors in QD lasers indicated

by Eqn (2.4)

The slope of fr versus (I-Ith)1/2 curve is defined as the modulation efficiency of

RF-modulated laser diodes, and is proportional to the square root of the product of

threshold gain and differential gain. In the linear regime ((I-Ith)1/2 up to 6 mA1/2), the

highest modulation efficiencies obtained among the lasers decrease monotonically with

p-doping from 0.54 GHz/mA1/2 (undoped), to 0.46 GHz/mA1/2 (40 holes/dot) but still

higher than previously reported results indicating excellent material quality[12]. Since the

injection efficiencies are very similar for both un-doped and p-doped devices, the

differential gain must be decreasing with the p-doping level to explain this trend. It is

conjectured that the increased internal loss with increased p doping more than offsets, the

larger maximum ground state gain and, consequently, causes gain saturation. To achieve

the same normalized current, the driving currents of p-doped lasers are much higher than

44

that of un-doped laser. The effect of carrier heating becomes severe at high bias condition

and enhances nonlinear gain saturation too [19]. To obtain a perspective on the non-linear

gain saturation in p-doped lasers, the evolution of the squared relaxation frequency versus

the output power is plotted in Fig. 2.6 The saturation power Psat that is listed in Table 2

can be extracted by curve-fitting these results with Eqns (2.4)-(2.5). The fitting function

was shown in the figure as an inset. It can be seen that the non-linear regime is more

pronounced when the p-type doping level is high. The Psat decreases from 90 mW for the

undoped wafer to 18.4 mW, indicating that the relaxation frequency of the p-doped

device saturates rapidly compared with the un-doped device. This also can be proof that a

high doping level may deteriorate modulation bandwidth of QD lasers. In Ref [12],

Fathpour et .al reported a consistent result that p-doping technique can only provide a

limited improvement on QD laser’s bandwidth after comparing the modulation response

between p-doped and un-doped 1.1um QD device. However, they attributed this result to

a larger fraction of holes occupying the QD wetting layer states instead of the lasing

states in the QD. Our results indicate that for large QD densities, this slight improvement

with p-doping actually reverses and becomes a detriment to the high speed performance

45

Fig. 2.5. Relaxation frequency versus the square root of the bias current above threshold of 1.2 mm-long cavity length un-doped and p-doped lasers.

46

Fig. 2.6 Squared relaxation frequency versus output power for four lasers the set of QD lasers with different p-doping level.

fr2

f r2

47

2.6. Small signal modulation response of 0.8 mm HR coated devices.

To confirm the observed trend with p-doping, the hi-speed performance of

p-doped QD lasers was further examined using 800-µm long RWG devices with a 95%

high-reflection (HR) coating on one facet only. For comparison, the relation between fr

and ( I-Ith)1/2 is plotted too in Fig. 2.7 for the four different lasers. Compared to the

1.2-mm as-cleaved lasers, these HR-coated lasers show larger maximum relaxation

frequencies equal to 5.0 GHz, 5.5 GHz and 4.3 GHz for the p-doped device set. Normally,

HR coating results in a decreased modulation bandwidth since it increases the photon

lifetime of the lasers. This bandwidth improvement in HR-coated devices is presumably

due to reduced gain saturation. The lower relaxation frequency of the wafer 619 lasers

compared to 618 could be attributed to a less efficient HR-coating. A comparison of the

modulation efficiencies in the linear regime (up to a (i-ith)1/2 ≅ 7) led to 0.60 GHz/ mA1/2,

0.58 GHz/ mA1/2 and 0.44 GHz/ mA1/2 for the three p-doped QD wafers. These results

further confirm that the differential gain of p-doped QD lasers decreases with doping

density in the range explored given a constant cavity length.

48

Fig 2.7 Relaxation frequency versus the square root of the normalized bias current of the

three doped lasers with one HR-coated facet and cavity length of 800 μm.

49

2.7. Summary

In conclusion, the static performance and modulation frequency response of

un-doped and p-doped InAs/GaAs QD lasers were studied in this chapter. The internal

loss increases with p-doping level from 7.5 cm-1 for the 20 holes/dot wafer to 10 cm-1 for

40 holes/dot wafer, which are much larger than the value of 2 cm-1 for un-doped lasers.

Although the maximum ground state gain of the p-doped laser is larger than that of

un-doped lasers and increases with p-doping level, the corresponding increase in internal

losses induces gain saturation and gain compression and, thus, degrades the high-speed

performance of p-doped QD lasers. The modulation efficiency and the highest relaxation

frequency of 1.2-mm cavity length lasers decrease monotonically with the p-doping level

from 0.54 GHz/mA1/2 and 5.3 GHz (un-doped wafer) to 0.46 GHz/mA1/2 and 3.6 GHz (40

holes/dot). The net result is that a p-type concentration in the range of 20 to 40 holes/dot

decreases the differential gain for lasers with constant cavity length. Based on

curve-fitting procedure, the saturation power is found to decrease with the p-type level

from 90 mW (un-doped) to 18.4 mW (40 holes/dot). The degrading of modulation

performance of p-doped device is attributed to higher gain saturation factor due to carrier

heating effect. More promising methods to improve the modulation bandwidth in QD

devices is improve the uniformity of dots, implement the gain lever effect, or employing

injection-locking. The last two will be studied in the next two chapters.

50

References

[1] D. Bimberg, N. Kirstaedter, N. N. Ledentsov, Z. I. Alferov, P. S. Kopev, V. M.

Ustinov, “InGaAs-GaAs quantum-dot lasers”, IEEE Journal of Selected Topics in

Quantum Electronics; vol.3, no.2, pp.196-205, 1997.

[2] M. Sugawara, N. Hatori, M. Ishida, H. Ebe, Y. Arakawa, T. Akiyama, K. Otsubo, T.

Yamamoto, Y. Nakata, “Recent progress in self-assembled quantum-dot optical

devices for optical telecommunication: temperature-insensitive 10 Gbs(-1) directly

modulated lasers and 40Gbs(-1) signal-regenerative amplifiers”, Journal of Physics

D-Applied Physics, vol.38, no.13, pp.2126-2134, 2005.

[3] K. Kamath, J. Phillips, H. Jiang, J. Singh, P. Bhattacharya, “Small-signal modulation

and differential gain of single-mode self-organized In0.4Ga0.6As/GaAs quantum dot

lasers”, Applied Physics Letters, vol.70, no.22, pp.2952-2953, 1997

[4] H. Su, L. F. Lester, “Dynamic properties of quantum dot distributed feedback lasers:

high speed, linewidth and chirp”, Journal of Physics D-Applied Physics, vol.38, no.13,

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[5] S. Krishna, J. Sabarinathan, K. Linder, P. Bhattacharya, B. Lita, R. S. Goldman,

“Growth of high density self-organized (In,Ga)As quantum dots with ultranarrow

photoluminescence linewidths using buried In(Ga,Al)As stressor dots”, Journal of

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[6] K. Matsuda, K. Ikeda, T. Saiki, H. Tsuchiya, H. Saito, and K. Nishi, “Homogeneous

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[7] D. R. Matthews, H. D. Summers, P. M. Smowton, M. Hopkinson, “Experimental

investigation of the effect of wetting-layer states on the gain-current characteristic of

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[8] O. B. Shchekin, D. G. Deppe, “The role of p-type doping and the density of states on

the modulation response of quantum dot lasers”, Applied Physics Letters, vol.80,

no.15, p.2758-2760, 2002

[9] P. Bhattacharya, S. Ghosh, S. Pradhan, J. Singh, Z. K. Wu, J. Urayama, K. Kim, T. B.

Norris, “Carrier dynamics and high-speed modulation properties of tunnel injection

InGaAs-GaAs quantum-dot lasers”, IEEE Journal of Quantum Electronics, vol.39,

no.8, p.952-962, 2003.

[10] Y. Li, T. J. Rotter, Y. C. Xin, A. Stinz, A. Martinez, K. J. Malloy and L. F.

Lester, “High Characteristic Temperature of p-doped InAs Quantum Dots-in-a-Well

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[11]. O. B. Shchekin, J. Ahn, D. G. Deppe, “High temperature performance of

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[12]. D. G. Deppe, H. Huang, O. B. Shchekin, “Modulation characteristics of

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[13]. M. Sugawara, K. Mukai, H. Shoji, “Effect of phonon bottleneck on

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pp.2791-2793, 1997

[14]. S. Fathpour, Z -T. Mi, P. Bhattacharya, “Small-signal modulation

characteristics of p-doped 1.1- and 1.3-mu m quantum-dot lasers”, IEEE Photonics

Technology Letters, vol.17, no.11, pp.2250-2252, 2005

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B. Ohnesorge, A. Forchel, “Optical transitions and carrier relaxation in self assembled

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[16]. W. W. Chow, S. W. Koch, “Theory of semiconductor quantum-dot laser

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53

[18]. R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, J. E. Bowers,

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54

Chapter 3 Gain-lever quantum dot lasers

3.1 Introduction

As was briefly discussed in chapter 1, the modulation bandwidth of direct modulated

semiconductor lasers is limited by the relaxation frequency. One of the physical origins of

this limitation comes from a link between threshold gain and differential gain. To obtain

high modulation bandwidth, the laser cavity is chosen as short as possible to obtain

shorter photon lifetime. This will cause the laser to operate at a high threshold gain

resulting in a small differential gain value, due to the non-linear relationship between

gain and carrier density in semiconductor QW and QD devices. Besides the bandwidth

consideration, the modulation efficiency also creates a great deal of concern in analog

communication systems. A typical RF link having a loss of 20-30 dB is a big challenge to

overcome for semiconductor laser applications. One of the alternative ways to improve

the modulation efficiency is to use gain-lever effect that implements a two-segment

contact and a common applied waveguide. The gain-lever technique was proposed by

Vahala et al in 1989, to improve the efficiency of modulated light conversion by RF

[1-3]. They demonstrated a 6-dB enhancement of the modulation response using an

optical gain-lever QW device. A 22-dB amplitude modulation (AM) was also realized by

Moore and Lau, using a 220-um QW device, with only a marginal increase in the

intensity noise [4, 5]. Since then, much research work has been conducted not only on

AM characteristics, but also wavelength tunability [6, 7] and frequency modulation (FM)

55

performance [8-10]. All of the previous work has been done on QW devices and 3-dB

bandwidth enhancement has yet to be reported.

In this chapter, the modulation response of a gain-lever quantum dot laser will be

discussed. The concept of the gain-lever device will be introduced, and then the new

response equation for gain-lever laser will be derived. The amplitude modulation

efficiency enhancement and 3-dB bandwidth enhancement is predicted theoretically and

demonstrated experimentally using un-doped and p-doped QD devices.

56

3.2. Modulation characteristic of gain-lever QD lasers

3.2.1 Basic concept of the gain-lever effect

Fig 3.1 Schematic of the two-section gain-lever semiconductor laser, with the variation of modal gain versus carrier density.

The schematic of a gain-lever laser is shown in Fig. 3.1. This two-section configuration

is formed by two separate contacts which are electrically isolated from each other. The

two sections can be biased individually even though they always share one continuous

optical cavity. The length of each section can be chosen freely. In the “normal” gain-lever

configuration, the short section, which is denoted as section (a), acts as modulation

section where the small RF modulation signal is applied on the top of a small DC pump

level. While the longer section, denoted as section (b), is usually DC biased only. The h is

57

the fractional length of the section (b). To operate the gain-lever device, section (a) is

biased at low gain level and section (b) is biased at a high gain level. This allows section

(b) to control the above-threshold operation of the whole device.

The total gain of the two-section laser is provided by both section (a) and (b). Before

threshold is reached, the total modal gain from the two sections is used to overcome the

cavity loss. When the device is biased above threshold, the total modal gain is firmly

clamped to the threshold gain, which is determined by the cavity loss. There is always an

insignificant amount of spontaneous emission coupled into the laser mode, which can be

neglected here. Above threshold, all injected carriers will be converted to an optical

output and will not contribute to gain. The gain clamping effect is one of the physical

foundations of the gain-lever device. The nonlinear relationship between gain and carrier

density of QW and QD devices is another physical basis to understand the gain-lever

device functionality. In Fig 3.1, the gain versus carrier density and the principal

configuration of the gain-lever device is shown. Due to the step-function-like density of

states, the ground state gain can’t linearly increase with injected carrier density. Instead,

it shows a saturation trend in the high carrier density region as shown in Fig. 3.1. Section

(a) is usually biased at the low gain region where the differential gain is larger, and

section (b) is biased at the high gain region and the differential gain is smaller. When a

small modulation signal is applied to section (a), a small change on carrier density is

observed. This is a result of current fluctuation and leads to a change of optical gain in

this section. Correspondingly, the gain in section (b) has to be changed in order to keep

58

the device clamped at the threshold value. Due to the nonlinear relationship between gain

and carrier density, there has to be a larger change in carrier density in section (b) to

compensate for the gain change. Consequently, the photon density is changed as well. As

a result, a larger modulated output can be realized by small signal modulation. This is

called the “gain-lever” effect.

3.2.2 Motivation for gain-lever QD lasers

As discussed above, the gain-lever effect requires gain clamping and a sub-linear

relationship between gain and carrier density. In low dimensional media, such as a QW,

this can be approximated by gain vs. injected current density. It is expected that active

media with a stronger gain saturation will generate a more significant gain-lever effect.

The optical gain is directly related to the density of states of the semiconductor material.

In QD materials, the density of states is a delta-function-like. Compared with QW

materials, which have a step-function-like density of states, QD active regions show a

stronger gain saturation effect and larger differential gain. In Fig 3.2, a typical optical

gain versus current density relationship for QW and QD materials is shown. The

maximum optical gain is smaller for QD due to the decreased density of state [11]. The

optical gain increases faster in QD and then saturates quickly. The differential gain of QD

device in the un-saturated region is larger than that of the saturated region. Consequently,

the devices fabricated from QD materials are promising to demonstrate the enhanced

gain-lever effect.

59

Fig 3.2 The typical optical gain versus current density relationship for QW and QD materials. QW is logarithmic and the QD demonstrates exponential saturation.

0 200 400 600 8000

10

20

30

40

50

Current density (A/cm2)

Opt

ical

Gai

n (c

m -1

)

Quantum wellQuantum dot

60

3.3. Novel response model of gain-lever lasers

3.3.1 The rate equation of gain-lever lasers

In this section, we will derive a new response model for the two section gain-lever

laser. The response equation of single section semiconductor laser was introduced in the

previous chapter is shown below:

⎥⎦⎤

⎢⎣⎡ +−+

∝2222

4

22

)2

()()2(11)(

fff

ff

fMr

r

c

πγτπ (3.1)

In Fig 3.3, the experimental data for the modulation response of a two-section

gain-lever QD device is plotted along with the curve fitted data using Eqn (3.1). The

response curve is taken when the current density of the two sections are different. It can

be seen that the conventional single-section response function cannot describe the

modulation response of the two-section laser very well. The first obvious drawback is the

damping rate. For a single section laser, the laser is biased uniformly across the device,

there is only one damping rate needed in a single section model, but in a two-section

structure, the modulation section and gain sections are always biased at different levels,

so that the differential gains of the two sections are different. Thus two damping rates are

required in the new model to describe the modulation response of the two-section device.

In order to derive the rate equations of the two-section laser, two separate differential

equations are needed to represent the fluctuation in carrier density during intensity

modulation. If we assume that the photon density is uniform in both the gain section and

61

modulation sections, then only one rate equation is required for the photon density

fluctuations. This assumption is valid because the two sections share the same optical

cavity even though they are under different carrier injection level. The electrical isolation

between the two sections only introduces some minor loss in the cavity and will not effect

the traveling of the optical wave. Therefore the rate equations of a two-section device can

be expressed as [4]:

SGN

eVI

dtdN

aa

aaa −−=τ

(3.1)

SGN

eVI

dtdN

bb

bbb −−=τ

(3.2)

[ ]p

baSShGhG

dtdS

τ−+−Γ= )1( (3.3)

Where S is the photon density, Ia,b, Na,b , τa,b and Ga,b are the injection current, carrier

density, carrier lifetime and unclamped material gains ( the group velocity is included

implicitly) respectively, Γ is the optical confinement factor, τp is photon lifetime, h is the

fractional length of the gain section, and d is the thickness of the active region. To

simplify the problem, we do not include the non-linear gain or any carrier transport effect

in the above rate equations at this time. The small signal solution of the equations is done

by first making the following substitutions:

tjbababa eiItI ω

,0,0, )( +=

tjbababa enNtN ω

,0,0, )( +=

tjbabababa enGGG ω

,0,00,0, ′+=

62

tjseStS ω+= 0)(

wherea

aa dN

dGG =′0 and

b

bb dN

dGG =′0 are the differential gains for the two sections. The

steady-state components are indicated by the subscript “0” and small AC components are

indicated by lower case letters. It should be noted here that G(N) is actually a sub-linear

function of the carrier density but not a linear function. However, in a steady-state

operation point, it can always be linearized locally, where G0’ is the differential gain at

the steady-state carrier density. For the small-signal carrier density variation n, G0’ is a

constant because the steady-state carrier density is clamped to the steady state value of

N0.

By substituting the small signal quantities into rate equations (3.1) through (3.3)

and setting the steady-state quantities to zero, the resulting small signal equations are:

000 SnGsGn

edi

nj aaaa

aaa ′−−−=

τω (3.4)

000 SnGsGn

edi

nj bbbb

bbb ′−−−=

τω (3.5)

[ ] [ ]p

babbaashGhGshnGhnGSsj

τω −+−Γ+′+−′Γ= 00000 )1()1( (3.6)

Under the steady-state condition, equation (3.3) gives the relation between Ga0 , Gb0 and

the threshold gain of the entire device (G0)as [4]:

pthba GGhGhG

τ1])1([ 000 ==Γ=+−Γ (3.7)

where Gth is the threshold modal gain. The second and third term of the RHS of Eqn. (3.6)

63

can be canceled by substituting Eqn. (3.7) into (3.6). Since in section “b”, there is no

modulation current, the expression of nb can be obtained as

0'0

0

/1 SGjsG

naa

bb ++

−=

τω (3.8)

By substituting Eqns. (3.4) and (3.8) into (3.6), the small signal response equation is

derived to be:

2123

00

)(/))(1(

)()(

AiAjedjhSG

js

ba

ba

a +++−−+−′Γ

=ωωγγω

γωω

ω (3.9)

Where A1, A2 are:

[ ] babbaa hGGhGGSA γγ+′+−′Γ= 000001 )1( (3.10)

[ ]hGGhGGSA abbbaa γγ 000002 )1( ′+−′Γ= (3.11)

γa and γb are defined as the damping rates in sections (a) and (b) respectively, that are

given by:

001 PGaa

a ′+=τ

γ (3.12),

001 PGbb

b ′+=τ

γ (3.13)

The first term in the damping rate expression is inversely proportional to the spontaneous

lifetime and the second term represents the inverse stimulated lifetime. When h = 0, Eqn.

(3.9) is reduced to the modulation equation for single-section lasers.

64

Fig 3.3. The modulation response of a two-section gain-lever QD laser, with curve-fitted data using a single section model.

65

3.3.2 Modulation efficiency enhancement

The gain-lever modulation efficiency or intensity modulation (IM) enhancement can be

obtained by taking the ratio of the modulation response from Eqn (3.9) to that of the

uniformly biased device ( when h = 0) at the low frequency limit, which is give by [4]:

( )QghRhisis

ab

b

ha

a

γγγ

η+−

===

)1(0

(3.14)

where 00 GGR a= , 00 GGQ b= , and 00 ba GGg ′′= .

In Fig (3.4), the evolution of the modulation efficiency enhancement versus the

fractional length h is plotted for differential gain values equal to 5, 10 and 15. For these

plots it is assumed that the modulation section is biased at R = 0.2. The modulation

efficiency enhancement increases monotonically with h when the other parameters are

kept unchanged. Therefore, the two-section device with a shorter modulation section is

preferred to achieve a high efficiency enhancement.

In the case of a very short modulation section (h close to 1), which is the device

configuration we use in this experiment, Eqn (3.14) is reduced to

0

0

00

00

ba

ab

bba

ab

GG

GGGG

′′

≈′′

=γγ

γγ

η (3.15)

When the gain-lever device is biased at a low level, the photon density inside the

cavity is small. As a result, the spontaneous damping term dominates the damping rate.

Therefore, Eqn. (3.15) is reduced to

66

0

0

bb

aa

GG

′′

≈ττ

η (3.16)

Thus, under low power level operation, the modulation efficiency enhancement comes

from two aspects: the ratio of the carrier lifetimes and the ratio of differential gains of the

two sections. Consider a lower photon density situation in which ba ττ = is a valid

approximation. The IM efficiency enhancement can be realized when 0aG ′ is larger than

0bG ′ . As we discussed above, the operation point of the gain-lever device is chosen where

the modulation section is biased at a high differential gain level and the gain section is

biased at a low differential gain level. Eqn (3.16) also indicates that even at the point

where differential gain is equivalent for both sections, like bulk semiconductor optical

devices, one can still obtain a substantial improvement on modulation efficiency. This

can be achieved by decreasing the carrier lifetime in the gain section. For this situation,

the gain section needs to be biased at a very high level in order to decrease the carrier

lifetime, which is not good for device reliability. It should be mentioned that lower

photon density (lower optical power) is not desired since the relaxation frequency and

3-dB bandwidth are small. The more interesting case is at high power levels. Also, it can

be seen that the differential gain ratio is actually key factor for gain-lever laser due to the

sublinear relationship between gain and current density.

Another extreme case of Eqn (3.15) is where the device is operated at very high

power. The inverse stimulated lifetime term dominates the damping rate since the photon

density is very large (the relaxation frequency is proportionally to photon density). This

67

reduces Eqn. (3.15) to:

10

0

000

000 ≈=′′′′

≈bbba

ab

GG

GGGGGG

η (3.17)

Clearly, there will be no modulation efficiency improvement at very high photon

density and large pumping asymmetry condition. The stimulated damping rate

counteracts the original low photon density IM efficiency enhancement. It is suggested

that the gain-lever device should operate at a relatively high power level to take

advantage of the improved modulation efficiency and maintain a useful level of output

power simultaneously where 00 ba GGg ′′=

Fig 3.4 Calculated modulation efficiency enhancement vary with h for g =3, 5 and 10,

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 16

8

10

12

14

16

18

20

h

Mod

ulat

ion

effic

ienc

y en

hanc

emen

t (dB

)

g=10

g=5

g=3

68

3.4 IM efficiency enhancement of p-doped gain-lever QD lasers

As we discussed in chapter 2, p-doped devices show high differential gain and

possibly higher bandwidth. In this section, the small signal modulation response on

p-doped gain-lever QD lasers is studied. The wafer structure and static performance of

p-doped devices is presented first, followed by a new gain model for QD devices is

introduced to extract the gain profile. Finally, the 8-dB modulation efficiency

enhancement of the gain-lever QD laser is presented using a RF modulation experimental

setup.

3.4.1 Wafer structure and device fabrication

The layer structure of the device under investigation is illustrated in Fig 3.5. It was

grown by the Molecular Beam Epitaxy (MBE) growth technique on n+ (001) GaAs

substrate. The active region consisted of 10 stacks of self-assembled InAs QDs covered

by 5-nm In0.15Ga0.85As QWs in a DWELL structure. The QW layers are separated by

33-nm GaAs spacers. A δ-doped layer is added in the GaAs barrier 10 nm above each QW.

The device’s cladding layers are step-doped 1.5-µm thick Al0.35Ga0.65As. The entire laser

structure is then capped with a 400-nm thick heavily carbon-doped GaAs. 50-μm-wide

broad area (BA) lasers were fabricated and then cleaved to different cavity lengths to

extract the G-J relationships. The two-section devices were fabricated by the standard

RWG processing technique. The two (multi)-section device processing flow chart is

shown in Fig. 3.6. The electrical isolation between each section was achieved by proton

69

implantation. The length of each isolated section is 0.5-mm.

Fig 3.5. The layer structure of p-doped QD lasers (wafer #224)

10X

GaAs C: 2e19 400nmAl.35Ga.65As/GaAs C: 3e18 20nmAl.35Ga.65As C: 1e18 1000nm

Al.35Ga.65As C: 5e17 500nm

GaAs 14nmIn.15Ga.85As quantum well 5nm

Al.35Ga.65As Si: 5e17 500nm

Al.35Ga.65As Si: 1e18 1000nmGaAs/Al.35Ga.65As Si:3e18 20nm

GaAs substrateGaAs Si:3e18 500nm

InAs quantum dots

GaAs 33nm

GaAs 9nmGaAs C: 5e17 10nm

10X

GaAs C: 2e19 400nmAl.35Ga.65As/GaAs C: 3e18 20nmAl.35Ga.65As C: 1e18 1000nm

Al.35Ga.65As C: 5e17 500nm

GaAs 14nmIn.15Ga.85As quantum well 5nm

Al.35Ga.65As Si: 5e17 500nm

Al.35Ga.65As Si: 1e18 1000nmGaAs/Al.35Ga.65As Si:3e18 20nm

GaAs substrateGaAs Si:3e18 500nm

InAs quantum dots

10X

GaAs C: 2e19 400nmAl.35Ga.65As/GaAs C: 3e18 20nmAl.35Ga.65As C: 1e18 1000nm

Al.35Ga.65As C: 5e17 500nm

GaAs 14nmIn.15Ga.85As quantum well 5nm

Al.35Ga.65As Si: 5e17 500nm

Al.35Ga.65As Si: 1e18 1000nmGaAs/Al.35Ga.65As Si:3e18 20nm

GaAs substrateGaAs Si:3e18 500nm

InAs quantum dots

GaAs C: 2e19 400nmAl.35Ga.65As/GaAs C: 3e18 20nmAl.35Ga.65As C: 1e18 1000nm

Al.35Ga.65As C: 5e17 500nm

GaAs 14nmIn.15Ga.85As quantum well 5nm

Al.35Ga.65As Si: 5e17 500nm

Al.35Ga.65As Si: 1e18 1000nmGaAs/Al.35Ga.65As Si:3e18 20nm

GaAs substrateGaAs Si:3e18 500nm

InAs quantum dots

GaAs 33nm

GaAs 9nmGaAs C: 5e17 10nm

70

Fig 3.6. The flow chart of the processing procedure for a two (multi)-section device.

PR

ICP etch for ridge waveguide

PR

Lithography for ridge waveguide(front view)

BCB

BCB Curing

BCB

BCB etch back with RIEp-type metal deposition (side view)Ion Implantation (side view)

n-type metal deposition (side view)

PR

ICP etch for ridge waveguide

PR

ICP etch for ridge waveguide

PR

Lithography for ridge waveguide(front view)

BCB

BCB Curing

BCB

BCB etch back with RIEp-type metal deposition (side view)Ion Implantation (side view)

n-type metal deposition (side view)

PR

Lithography for ridge waveguide(front view)

PR

Lithography for ridge waveguide(front view)

BCB

BCB Curing

BCB

BCB Curing

BCB

BCB etch back with RIE

BCB

BCB etch back with RIEp-type metal deposition (side view)p-type metal deposition (side view)Ion Implantation (side view)Ion Implantation (side view)

n-type metal deposition (side view)

71

3.4.2 Static characterization and gain measurement

To perform the gain-lever experiment, it is important to get the whole spectrum

for the relationship between gain and current density. This relationship can be extracted

based on the fact that threshold modal gain is equal to the total cavity loss at threshold.

Therefore, the broad area lasers were fabricated first for this purpose. The BA samples

were cleaved to different cavity length ranging from 0.75-mm to 2.8-mm. The lasers with

cavity length shorter than 0.75-mm cannot sustain ground state lasing. The cavity

dependent output power versus current ( P-I ) characteristics were measured under pulsed

condition ( 500-ns pulse width and 1% duty cycle). We can calculate the differential

quantum efficiency ηd from this set of P-I curves. The trend of 1/ηd versus cavity length

is shown in Fig 3.7. The internal loss, αi, and the internal quantum efficiency, ηi, can be

calculated by fitting the data to 1/ηd = 1/ηi [1- αiL/ln(R)], where L is the cavity length and

R = 0.32 is the reflectivity of the laser facets. From the calculation, ηi is 48% and the

internal loss αi is 2.7 cm-1.

72

Fig 3.7. The evolution of inverse differential efficiency with cavity length for p-doped QD lasers. The internal loss and injection efficiency are calculated by curve fitting the measured data.

4.0

3.5

3.0

2.5

2.0

1/η d

0.300.250.200.150.100.05

Cavity Length (cm)

ηi = 0.48

αi = 2.7 cm-1

73

The threshold modal gain can be calculated using the fact that modal gain is equal to

the sum of internal loss and mirror loss at the threshold, i.e.: mithG αα += . The mirror

loss is expressed as ⎟⎠⎞

⎜⎝⎛=

RLm1ln1α . The calculated Gth with threshold current density is

plotted in Fig. 3.8 and the experimental data is expressed as blue dots.

The data in Fig 3.8 offers the isolated points for the G-J relationship. However, in

the two-section configuration, the currents of each section could be far beyond the current

range shown in this figure. Thus we need an accurate gain model to curve fit this

experimental data. Equation (3.18) is an empirical gain model, which was used to

describe the G-J behavior in QD materials [9]:

⎟⎟⎠

⎞⎜⎜⎝

⎛−−−= ))1(2lnexp(1max

tr

th

JJ

GG (3.18)

where Gmax is the maximum gain for ground state lasing in the quantum dot media, and

Jth, Jtr are the threshold and transparency current densities, respectively. This model

works well with un-doped QD materials. In Fig 3.8 (a), the calculated modal gain data is

plotted as a function of threshold current density, and the data is curve-fitted using Eqn

(3.18). It was found that the exponential threshold current density dependence in this

mode did not fit very well with the experimental data. The exponential model was

originally derived for un-doped QD materials, which have a stronger gain saturation

effect. However, for this p-doped QD material, this model overestimates the saturated

gain. In Ref [13], a more accurate model with square-root current density dependence is

derived by our research group, which is given by:

74

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

+= 12)( max

trJJJGJG (3.19)

It is known that the optical gain is a function of wavelength. Eqn (3.19) is actually a

function of the peak gain varied with current density. In a real device, the gain peak shifts

towards shorter wavelengths (blue shift) as current density increases due to the band

filling effect. Using Eqn (3.19) the calculated Gth-J data was curve-fitted and the

maximum gain and transparency current density were calculated to be 86 cm-1 and 232

A/cm2 respectively. It can be seen that Eqn (3.19) fits better than the exponential model.

As we discussed in chapter 2, the p-doped technique helps increase the ground state gain

in QD media. The data in the Fig 3.8 also shows that the gain does not saturate strongly

as expected in the current range we investigated.

75

Fig. 3.8 The calculated threshold modal gain as a function of threshold current density. The data was curve-fitted using (a) the exponential gian model, (b) new square-root gain model.

25

20

15

10Mod

al g

ain

Gth

(cm

-1)

700600500400Threshold current density Jth (A/cm2)

25

20

15

10Mod

al g

ain

Gth

(cm

-1)

700600500400Threshold current density Jth (A/cm2)

76

3.4.3 Experiment setup for dynamic characterization of p-doped gain-lever QD laser

The total length of the two-section laser diode for the intensity modulation

experiment is 1.5-mm long. The modulation section is 0.5-mm long so that the fractional

length h is 2/3. Figure 3.9 shows the P-I characteristics of the device under uniform

bias. The threshold current is 35.5 mA at 20 0C. The lasing spectrum is shown in Fig

3.10. The peak wavelength is 1.29 μm.

The high-speed experimental setup is shown in Fig 3.11. It is similar to the one we

described in chapter 2, except two precision current sources are used to provide the

current flow into each section. A DC signal and small microwave signal are applied to

section (a) from port 1 of the HP8722D vector network analyzer. The section (b) is DC

biased only. The coupling efficiency to the lensed fiber was measured to be 10%.

It is necessary to clarify some terms we use to describe the gain-lever experimental

results. The modulation efficiency enhancement was measured by comparing the

modulation responses for uniform and asymmetric pumping cases. Uniform pumping

means the two sections have equal current density. For the specific device we tested, the

cavity length ratio of the two sections is 2:1, so the uniformly pumping requires the bias

current ratio to be 2:1 as well. The asymmetric pumping situation corresponds to the case

where the two sections have different current densities. The criteria to determine the

current ratio of the two sections is to keep the output power similar to the uniformly

pumping case. In our actual experiment, the current modulated section is set first, then

77

the current of the gain section was adjusted to maintain an output power equal to the

uniformly pumped case. Equal output power is considered to be the valid experimental

condition for comparisons of different pumping scenarios

. Fig 3.9 P-I curve of the gain-lever device under the uniformly biased condition

Fig 3.10 The lasing spectrum of the p-doped gain-lever RWG laser.

1.2

1.0

0.8

0.6

0.4

0.2Lasi

ng P

ower

(mW

) / F

acet

5045403530

Current I (mA)

Total Cavity Length L= 1.5 mm Ridge Width W=3 μmIth=35.5 mA @ 20°C

-50

-40

-30

-20

-10

0

Pow

er (d

Bm

)

1.401.351.301.251.20

Wave Lenght, λ (μm)

λp =1.29 μm

78

Fig 3.11 The high-speed testing set up for dynamic characterization of the p-doped gain-lever laser.

HP-8722Network Analyzer

Current Source

QD Device

Intensity Modulation

SM Optical Fiber

45GHz Hi-speed Photodetector

Lensed Fiber

Port 2

Port 1HP-8722Network Analyzer

Current Source

QD Device

Intensity Modulation

SM Optical Fiber

45GHz Hi-speed Photodetector

Lensed Fiber

Port 2

Port 1HP-8722Network Analyzer

Current Source

QD Device

Intensity Modulation

SM Optical Fiber

45GHz Hi-speed Photodetector

Lensed Fiber

Port 2

Port 1

79

The modulation response of the uniformly-pumped gain-lever laser was examined

first to get a general idea of the effect of the spontaneous damping term compared to the

total damping rate for this p-doped QD laser. Fig 3.12 gives response curves at different

biases. The highest current is 120-mA which is about 4 times greater than threshold. The

experimental data was curve-fitted using the single-section response equation. The

maximum relaxation frequency is calculated as 5-GHz. Based on curve fitted data, the

evolution of damping rate, γuni, versus the square of relaxation frequency fr is plotted in

Fig 3.12. The relationship between γuni and fr is

SGfc

pc

uni ′+=+=τ

τπτ

γ 141 2r . (3.20)

Using the above equation, the experimental data in Fig 3.12 is curve-fitted and the

variation of γuni as a function of fr2 is plotted in Fig 3.13. The linear relationship between

γuni and fr2 indicates that the gain saturation effect is not significant in this testing range.

This is consistent with our gain data in the last section. Fig 3.13 shows how the damping

rate, especially the stimulated damping component, varies with the power level. Although

the stimulated damping component is no more larger than about 4X greater spontaneous

damping rate for the uniformly pumping case, it should be realized that the stimulated

damping rate could be dominant due to high photon density or differential gain in the

asymmetric pumping case. The y-axis intercept of the fitting curve is the spontaneous

damping rate (8-GHz, which corresponds to 0.12-ns differential carrier lifetime). This

value is relatively small compared to the typical carrier lifetime values of 1-ns for

80

un-doped lasers. However, since τ decreases with doping level, this value is not too

surprising in our p-doped QD device.

Fig 3.12 Modulation response of the gain-lever laser under different uniformly bias condition. Fig 3.13. The evolution of damping rate with relaxation frequency under different uniformly bias conditions.

-90

-85

-80

-75

-70

-65

-60

Res

pons

e (d

B)

108642

Frequency (GHz)

I=42 mA 60 mA 75 mA 90 mA 105 mA 120 mA

81

3.4.4 Modulation efficiency enhancement

It is known that the gain-lever device should be biased in such a way that the

differential gain ratio is as large as possible to obtain the largest modulation efficiency

enhancement. The differential gain ratio can be calculated according to Eqn. (3.19) after

Ga0 and Gb0 were determined from Fig 3.8. It is clear that Ga0 and Gb0 are two

fundamental parameters to characterize this asymmetric pumping scenario. Following

Moore’s and Lau’s convention, we choose Ga0, for this work.

The Ga0 and Gb0 can be calculated as

)()1()(

)()(0

aabb

thaaaa JGhJhG

GJGJG

−+= (3.20)

)()1()()(

)(0aabb

thbbbb JGhJhG

GJGJG

−+= (3.21)

where, Ga0 and Gb0 are the threshold gains in section (a) and sections (b) respectively, Ga

and Gb are the unclamped gains in the respective sections, Gth is the threshold gain of the

device.

In Fig. 3.14, modulation responses for the uniform and asymmetric pumping cases at

a constant power level of 3 mW/facet are plotted. A modulation efficiency enhancement

as high as 8-dB was observed for our two-section QD device when the shorter section

was biased such that Ga0/Gth=0.56 (note: Ga0/Gth=1 corresponds to the uniform pumping

case). As Ga0 increases, Ga0’ decreases. According to Eqn. (3.17), the modulation

efficiency enhancement decreases as shown in the figure.

82

According to previous research on the modulation efficiency enhancement [7]:

0

0

b

a

b

a

uniform

gainlever

GG

′′

==ττ

ηη

η (3.22)

Making the reasonable assumption that the carrier lifetimes τa and τb are very close

to each other, the 8-dB improvement in η corresponds to a differential gain ratio of 2.5.

This value is surprising to us since it is not as large as being expected. The reason is that

in p-doped material, the gain does not saturate strongly with current density, as pointed

out in the last section.

Fig 3.14 Modulation efficiency enhancement of p-doped QD gain-lever lasers

-85

-80

-75

-70

-65

-60

-55

-50

Res

pons

e (d

B)

654321

Frequency (GHz)

Uniformly Ga0/G0=1 1: Ga0/Gth=0.56 2: Ga0/Gth=0.68 3: Ga0/Gth=0.74 4: Ga0/Gth=0.86

Power @ facet =3 mW h=0.67

83

3.5 Relative modulation response equation

The relative modulation response function can be derived by taking Eqn (3.9)

normalized to the response at zero frequency and is expressed as follows:

2123

2

)()(

)0()0()()(

)(AAii

iA

is

is

Rba

b

a

a

+++−−+

==ωωγγω

γωωω

ω (3.23)

It is difficult to obtain a clear physical understanding of the above equation, without

applying some approximations. Considering the low photon density case is not desired,

the device in our experiment is always running at relatively high power level. Thus, a

high photon density approximation can be made.

Under a high photon density approximation, the spontaneous damping term is

neglected in γa and γb . The parameters A1 and A2 are reduced to

barA γγω += 21 (3.24),

p

abAτγγ

=2 (3.25)

where frequency ωr is derived from Eqn (3.9) under the high frequency approximation. It

is given by:

ω r = ΓP0 Ga 0 ′ G a 0(1− h) + Gb 0 ′ G b 0h[ ]( )12 (3.26)

Substituting Eqns (3.24) and (3.25) into Eqn (3.23), the new relative modulation response

equation in terms of frequency is given by:

84

( )2

32

2

22

3

22

32

428

218

)(

⎥⎦

⎤⎢⎣

⎡−⎥⎦

⎤⎢⎣⎡ ++

⎥⎥⎦

⎤

⎢⎢⎣

⎡+−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛

=

ffff

f

fRba

rbap

ba

bp

ba

πγγ

πγγ

τπγγ

γπ

τπγγ

(3.27)

where the relation ω = 2πf is used.

In Eqn (3.27), the denominator has three poles instead of the usual two associated

with a single section laser diode as shown in Eqn (3.1), which has a quadratic dependence

of frequency. Also, in this equation the two different damping rates are included to

describe the damping effect on the resonance frequency and modulation response. We use

this equation to fit the same experiment data that is used in Fig 3.1, the result is shown in

Fig 3.15. Now we can specify that this response curve is taken at Ga0/G0= 0.5 and the

power level is 14-mW (a very high power level). Apparently, the new model fits better

with two-section response than a single section model.

85

Fig 3.15. The modulation response of a two-section gain-lever QD laser, with fitted curves using single-section and new two-section model

One may argue that good curve-fitting comes from an additional damping rate fitting

parameter in the two-section model, to further explore the validation of the relative

two-section response equation, in Fig 3.16 and 3.17, the dependence of the normalized

resonance frequency fr/fr0 on the normalized gain in the modulation section is plotted. The

fr are curve-fitted by the one-section model and new two-section model, respectively. The

normalized resonance frequency is obtained by the relaxation frequency of the

asymmetrically pumped case over the relaxation frequency of the uniformly pumped case.

Fig 3.16 shows the data that is curve fitted using the single-section model, while Fig 3.17

presents the two-section model data. The normalized gain is calculated in the same

-16

-12

-8

-4

0R

espo

nse

(dB

)

108642

Frequency (GHz)

Experimental Data Curve fittited using Two-Section Model Curve fittited using Single-Section Model

86

method. Due to the parabolic shape of the p-doped QD gain characteristics, the

gain-differential gain product in the two sections must staying relatively constant, i.e.,

Ga0G′a0 ≅ Gb0G′b0. According to Eqn (3.21), the resonance frequency fr, should remain

almost the same for different pumping values at a constant output power. This trend can

be verified by the data in Fig 3.17. However, in Fig 3.16, the sudden increase in the

resonance frequency for values below Ga0/Gth = 0.4 seems to be totally unphysical. We

can conclude that for values below Ga0/Gth = 0.4, the conventional single-section model is

no longer valid for the two-section configuration.

87

Fig 3.16 Normalized resonance frequency as a function of normalized gain in the modulation section plotted based on the one-section model.

Fig 3.17 Normalized resonance frequency as a function of normalized gain in the modulation section plotted based on the new two-section model

1.1

1.0

0.9

0.8

0.7

f r /

f r0

1.00.80.60.40.20.0Ga0/Gth

Power@ facet: 14 mW

1.1

1.0

0.9

0.8

0.7

f r / f

0

1.00.80.60.40.20.0Ga0/Gth

Power @ facet: 14 mW

88

3.6 Bandwidth enhancement in the gain-lever device

Above all, we just talked about IM modulation efficiency enhancement. The

question that is put forth at the beginning of this chapter still remains: Is it possible that

the gain-lever device can improve the modulation bandwidth?

We know under the high photon density approximation that the stimulated emission

contribution to the damping rate is dominant. The ratio of the damping rate is equal to the

ratio of the differential gain, i.e:

b

a

b

a

GG

gγγ

=′′

=0

0 (3.28)

Consider an extreme asymmetrically pumped case, in which Ga0 = 0 and h ≈1.

Under this circumstance, the gain section occupies most of the device. The damping rate

of the gain section, γ b, is approximated as the damping rate of the uniformly pumped

device, then we have

2runib Kf=≈ γγ (3.29)

where K is the damping rate over the square of the relaxation frequency for a single

section device. Eqn.(3.27) can be modified to be

2

32

422

222

4

2

2

24

2

42)1(

2

212

)(

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡++⎥

⎦

⎤⎢⎣

⎡ +−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

=

fffgK

ffKfggKf

KffgKf

fRr

rrr

r

r

πππ

ππ

(3.30)

where g is the ratio of the differential gain. In Fig 3.18, the calculated response curve is

89

plotted based on the above equation for g ＝1, 3, 5 and 7. g =1 corresponds to the

uniformly pumping case. As g increases, the 3-dB bandwidth increases as well. The

relaxation frequency is set at 4-GHz, which is a typical value for our p-doped device. The

similar bandwidth enhancement was also demonstrated by two-section DFB lasers [14].

Although p-doped devices can provide a larger ground state gain and differential gain,

it is not favorable for gain-lever applications, which needs strong gain saturation to

produce a larger differential gain ratio instead of the absolute value of differential gain.

Therefore, larger IM efficiency and 3-dB bandwidth enhancement are hard to achieve. In

the next section, we will continue to study the gain-lever device using an un-doped QD

laser, a higher improvement is expected.

Fig 3.18 The simulation of the modulation responses of a gain-lever QD laser which is under extreme asymmetrically pumping.

90

3.7 Un-doped gain-lever QD device

3.7.1 Gain measurement using the segmented-contact method.

In previous sections, we introduced an accurate gain versus current density

relationship which is critical to perform the gain-lever experiment. There are several

methods to measure the G-J relation in semiconductor lasers. Hakki and Paoli first

determined the gain from the depth of modulation, i.e., the peak-to-valley ratio, in the

amplified spontaneous emission (ASE) caused by the Fabry–Perot resonances of the laser

cavity. For an appropriate evaluation of the gain, the Hakki-Paoli method requires a high

wavelength resolution for the measurement system, and it is only accurate below the laser

threshold. In previous sections for p-doped devices, due to the issue of device availability,

the G-J relationship was obtained by measuring the threshold gain of the lasers with

different cavity lengths. However, since this involves cleaving and preparing many

devices, it is not easy to get an arbitrary point on the G-J curve, and we lack the

information about the variation of gain with wavelength. In this section, for un-doped QD

devices, we use an improved segmented contact method to measure the gain spectra.[15].

This technique does not require high spectral resolution, is compatible with optical fiber

butt coupling, and can extract the gain over a wide range of conditions. The added benefit

of the multi-section layout is that one can vary the ratio of the modulation and gain section

lengths without switching to another device

The principal of segmented contact method is illustrated in Fig. 3.19. The

91

multi-section device consists of three forward biased sections and an absorber section for

eliminating all the back-reflected light. The amplified spontaneous emission (ASE) is

measured when the first section, both the first and second section, and all three sections

are biased at the same current density. Mathematically, it is expressed as:

( )

( )

( ) 33

22

1

1)3exp(

1)2exp(

1)exp(

−

−

−

+−⋅=

+−⋅=

+−⋅=

leakL

leakL

leakL

ILGGSP

ILGGSP

ILGGSP

(3.31)

Where G is the net modal gain, S is the pure or un-amplified spontaneous emission

intensity, P is the amplified spontaneous emission and L is the length of each section. Ileak

is the unguided spontaneous emission intensity. Under the assumption that Ileak is the

same for the different pumping configurations as described above, a simple expression

for G is obtained as:

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−−

= 1ln1

2

3

LL

LL

IIII

LG (3.32)

3.7.2 Wafer structure and device configuration

The un-doped QD devices used in the following set of measurements contain a 10-stack

InAs/InGaAs DWELL active region that emits around 1.23-μm. The laser structure was

grown by molecular beam epitaxy (MBE) on a (001) GaAs substrate. The multi-section

device was fabricated following the same procedure that is described in section 3.3. The

length of each section is 0.5-mm and the total length of the device is 7 mm. Fig 3.20

92

illustrates the schematic of the segmented-contact device layout. The long absorber was

achieved by wire-bonding multiple sections together and is used to minimize the

back-reflected light.

Fig. 3.19 An illustration of the basic operation procedure for the segmented-contact device

Fig 3.20. Schematic of the segmented contact device. The long absorber is achieved by wire-bonding multiple section together and used to minimize back reflection.

i

PL

2i

P2L

3i

P3L

i

PL

i

PL

2i

P2L

2i

P2L

3i

P3L

3um

Absorber

93

. Figure 3.21 and 3.22 show the net modal gain data for a 10-stack undoped QD laser

media which is used for the gain lever device. It can be seen from Fig. 3.23 that this

material shows a unique camel-back gain characteristic under saturation at current

densities higher than 18 mA/section (equivalent to 1200 A/cm2). In other words, the

difference in the maximum gain between the ground state and excited states is very small.

Figure 3.24 show the G(J) curves of the ground and excited states by tracking the gain at

a lasing wavelength of 1236-nm and 1172-nm, respectively. Both curves saturate at

approximately 10.5-cm-1. Compared with p-doped samples, this un-doped sample has

smaller ground state gain, but a much stronger gain saturation effect before the peak gain

moves to the excited state. Larger modulation efficiency and bandwidth enhancement are

expected.

94

Fig. 3.21. Net modal gain spectra of a 10-stack undoped QD device

Fig. 3.22 Dependence of the net modal gain on injected current density in the QD device.

95

3.7.3 AM modulation for the un-doped QD gain-lever laser.

The two devices used for high-speed characterization are 1.25-mm (device #1) and

1.5-mm (device #2) long, and included 5 and 6 electrically-isolated sections, respectively.

The P-I relations of the uniformly pumped two devices are plotted in Fig 3.23. The

benefit of the multi-section layout is that one can vary the ratio of the modulation and gain

section lengths without switching to another device. For example, we can use one device

to perform the modulation measurement as if we had access to three devices with h =

0.83, 0.67, 0.5, respectively (corresponding to modulation section lengths of 0.25-mm,

0.5-mm and 0.75-mm for the 1.5-mm cavity device). The AM modulation experiment is

Fig 3.23. L-I characteristics of two uniformly biased un-doped QD devices.

96

performed on #1 device first when h is chosen as 0.8. In Fig 3.24, modulation

responses for the uniform and asymmetric cases at a constant power level of 4.5

mW/facet are plotted. From the solid curve in the figure, a 20-dB modulation efficiency

enhancement is obtained for device #1 when the shorter section is biased just below

transparency. It is shown that the injected current when the shorter section decreases, the

modulation efficiency enhancement rises due to the increasing gain-lever.

Figure 3.25 shows the modulation efficiency enhancement as a function of the

normalized gain, Ga0/G0, in the modulation section for different fractional lengths h in

device #2. The DC bias current must be changed as the modulation section gets longer in

order to keep the same current density applied on the section. As h decreases, it can be

seen that the modulation efficiency enhancement increases for a given normalized gain in

the modulation section. The reason for this behavior is that the shrinking gain section

must compensate for the larger gain deficit, which in turn enhances the asymmetry

between the 2-sections. Since the current density in the modulation section stays roughly

constant at a given normalized gain, the gain section must be biased at a higher current

density to maintain the same output power. From the G-J curve obtained in Fig. 3.20, the

differential gain of section “b” (Gb0’) is smaller when the current density is high.

Therefore, the modulation efficiency enhancement gets larger according Eqn. (3.15).

Similarly, for a fixed h value, when the pump level in section “a” is increased (higher

normalized gain), the differential gain becomes smaller, so the modulation efficiency

enhancement decreases as the normalized gain increases. We should notice here that the

97

current density of the modulation section cannot be reduced too much. Otherwise, the

bias current of the gain section must be very high to keep the same output power, which

may cause an undesirable mode hop to the excited state transition of the quantum dot.

Fig 3.24. The modulation responses for the uniform and asymmetrically pumped cases in the un-doped QD laser.

Fig 3.25 The modulation efficiency enhancement depends on normalized gain Ga0/G0 for different h value.

98

3.7.4 Bandwidth enhancement in the un-doped device

In section 3.6, we derived that for a very asymmetrically pumped condition, the

gain-lever device will show a 3-dB bandwidth enhancement. For the p-doped material,

since gain does not saturate strongly, the bandwidth enhancement could not be

demonstrated. However, from Fig 3.19, we know that this un-doped device will have a

very strong gain saturation effect with current density; it is possible to demonstrate a

3-dB bandwidth enhancement based on this material. In Fig 3.26, and Fig 3.27, the

modulation response of device #1 is plotted for the uniform and asymmetric cases at a

constant power level of 6.5-mW/facet and 7.9-mW/facet, respectively. The damping rates

γa and γb can be obtained by curve-fitting the experimental data using Eqn. (3.20). In Fig

3.26, the ratio of the 3-dB bandwidth of asymmetric pumping to uniform pumping case is

1.3. This is consistent with the theoretical curve of g = 3 (shown in Fig.3.18). In Fig 3.27,

the damping rate ratio is calculated as 6.75, the 3-dB bandwidth ratio is 1.7. From Fig

3.18, it can be found that when g = 7, f3dB/f3dB_uni = 2. Therefore, the gain-lever device can

demonstrate bandwidth enhancement for certain conditions. In Fig 2.7, the 3-dB

bandwidth of the asymmetrically biased case is about 5-GHz, which is about 3X higher

than the relaxation frequency. This is the first time such an enhancement has been

reported. However, it should be noticed that the operational requirement is very strict.

This will limit the practical application of the device, alternative ways to improve the

bandwidth need to be explored.

99

Fig 3.26 The modulation responses for device #1 biased asymmetrically and uniformly. The power lever is 6.5 mW/facet. The ratio of 3-dB bandwidth of the asymmetrically to uniformly pumping case is 1.3.

Fig 3.27 The modulation responses for device #1 biased asymmetrically and uniformly. The power level is 7.9 mW/facet. The ratio of 3-dB bandwidth of the asymmetrically to uniformly pumping case is 1.7.

-30

-20

-10

0

10

20

30

Res

pons

e (d

B)

654321

Frequency (GHz)

Asymmetrically γa=8.5 GHzγb=2.9 GHzfr=1.8 GHz

Uniformly fr=2.14 GHzγuni=9.05 GHz

Asymmetrically pumped Uniformly pumped

-30

-20

-10

0

10

20

30

Res

pons

e (d

B)

6543210

Frequency (GHz)

Asymetricallyγa=13.23 GHz

γb=1.96 GHzfr=1.66 GHz

Uniformlyfr=2.27GHzγuni=9.87 GHz

Asymetrically pumped Uniformly pumped

100

3.8 Summary

The gain-lever laser is suggested as a promising tool to increase the modulation

efficiency of semiconductor lasers in analog optic links. In this chapter, the modulation

response characteristics of the gain-lever quantum dot lasers were studied. The 8 dB

modulation efficiency enhancement is achieved using p-doping Due to the stronger gain

saturation, the un-doped device shows a higher gain-lever effect over the p-doped device.

A 20 dB enhancement of the modulation efficiency is demonstrated by the un-doped QD

laser. Under the high photon density approximation, a new relative response equation

which includes two damping rates was developed for the two-section gain-lever laser.

The new model has three poles in the denominator instead of two like the classical

single-section equation. This allows a better fit with the experimental response curves

for the gain-lever lasers. A 1.7X 3-dB bandwidth improvement is theoretically predicted

by the new model and realized in the un-doped QD gain-lever laser under an extreme

asymmetrically biased condition. It is also demonstrated for the first time that in a

gain-lever laser, the 3-dB bandwidth can be 3X higher than relaxation frequency instead

of 1.55X in a typical single section laser.

101

References:

[1]. K. J. Vahala, M. A. Newkirk, T. R. Chen, “The optical gain lever - a novel gain

mechanism in the direct modulation of quantum well semiconductor-lasers”, Applied

Physics Letters; vol. 54, no.25, pp.2506-2508, 1989

[2]. C. P. Seltzer, L. D. Westbrook, H. J. Wicks, “The Gain-Lever effect in InGaAsP/InP

Multiple-Quantum Well Lasers”, Journal of Lightwave Technology, vol.13, no.2, pp.

283-289, 1995.

[3]. K. Y. Lau, “Passive microwave fiberoptic links with gain and a very low-noise figure,

IEEE Photonics Technology Letters; vol.3, no.6, p.557-559, 1991

[4]. N. Moore, K. Y. Lau, Ultrahigh efficiency Microwave signal transmission using

tandem-contact single quantum well GaAlAs lasers, Applied Physics Letters, vol. 55,

no.10, p.936-938, 1989

[5]. D. Gajic, K. Y. Lau, “Intensity noise in the ultrahigh efficiency tandem-contact

quantum-well lasers”, Applied Physics Letters; OCT 29 1990; v.57, no.18, p.1837-1839.

[6]. K. Y. Lau, “Broad wavelength tunability in gain-levered quantum-well

semiconductor-lasers”, Applied Physics Letters, vol. 57, no.25, pp.2632-2634, 1990.

[7]. G. Griffel, R. J. Lang, A. Yariv, “Two-section gain-levered tunable

distributed-feedback laser with active tuning section” , IEEE Journal of Quantum

Electronics; vol. 30, no.1, pp.15-18, 1994

[8]. K. Y. Lau, “The inverted gain-levered semiconductor-laser direct modulation with

102

enhanced frequency-modulation and suppressed intensity modulation”, IEEE Photonics

Technology Letters; vol. 3, no.8, pp.703-705, 1991

[9]. K. Y. Lau, “Frequency-modulation and linewidth of gain-levered 2-section single

Quantum-well lasers”, Applied Physics Letters; vol. 57, no.20, pp.2068-2070, 1990

[10]. H. Olesen, J. I. Shim, M. Yamaguchi, M. Kitamura, “Proposal of novel gain-levered

mqw dfb lasers with high and red-shifted fm response”, IEEE Photonics Technology

Letters; vol. 5, no.6, pp.599-602, 1993

[11]. L. F. Lester, A. Stintz, H. Li; T. C. Newell, E. A. Pease, B. A. Fuchs, K. J. Malloy,

“Optical characteristics of 1.24-mu m InAs quantum-dot laser diodes”, IEEE Photonics

Technology Letters, vol. 11, no.8, pp.931-933, 1998

[12]. Y.–C. Xin, “Long wavelength Quantum Dot Lasers on GaAs: New materials and

modal gain analysis”, Master Thesis, University of New Mexico, 2002.

[13]. B.W. Hakki and T. L. Paoli, “Gain spectra in GaAs double-Heterostructure injection

lasers,” J. Appl. Phys., vol. 46, pp. 1299–1305, 1975.

[14]. E. Goutain, J. C. Renaud, M. Krakowski, D. Rondi, R. Blondeau and D. Decoster,

“30 GHz bandwidth, 1.55μm MQW-DFB laser diode based on a new modulation

scheme”, Electron. Lett. vol. 32, pp. 896-897, 1996.

[15] Y.-C. Xin, H. Su and L. F. Lester, “Determination of optical gain and absorption

of quantum dots with an improved segmented contact method”, SPIE Photonics West

Annual. Mtg,. San Jose, CA, 2005

103

Chapter 4. Modulation Characteristics of Injection-locked

Quantum Dash Lasers

4.1 Introduction

In the previous chapter, we already demonstrated that the gain-lever device can offer

bandwidth enhancement under some certain bias conditions. Generally speaking, the

gain-lever device is a constraint coupled oscillator system with particular constraints.

Two electrically isolated sections share a common optical cavity, thus the phase of two

sections are automatically matched, while the photon density related component of the

damping rate of the two sections can not vary randomly, especially for the damping rate

of the gain section. In order to enhance the bandwidth, the gain-lever device needs to be

extremely asymmetrically pumped and operated at very high power level, which is not

healthy for device reliability. An injection locking laser, which is another coupled

oscillator system, is expected to demonstrate bandwidth enhancement in semiconductor

lasers [1-3]. In this chapter, injection locked lasers are studied theoretically and

experimentally. The 3-dB bandwidth enhancement is demonstrated using 5-layer

quantum dash (QDash) Fabry-Perot (F-P) laser under different injection power ratio and

frequency detuning. As much as 4 times bandwidth enhancement was demonstrated. The

modulation responses were examined when different lasing modes were injection-locked.

It was found that the injection-locking laser can share the same modulation response

104

function as the with gain lever laser in a particular injection strength range. The

relaxation frequency was derived from this equation and the maximum achievable 3-dB

bandwidth in the period 1, non-linear regime.

4.2 Basic concept of injection-locking

4.2.1 Injection locking concept and history

The injection locked system can be very complicated but the basic concept is simple.

An injection locked system consists of two coupled lasers which are assigned as a master

and a slave laser. The schematic of the injection locked laser is shown in Fig 4.1. The

light emitted from the master laser is fed into the slave laser. When the frequency of the

master laser is very close to the lasing mode of the slave laser, the slave laser can oscillate

at the frequency of the master laser and keep a constant phase shift. In strong injection

locking system, the master laser is usually a narrow linewidth, tunable high power laser,

thus either tunable DFB lasers or an external cavity laser are good candidates.

Fig 4.1 The schematic of optical injection locking system.

Master SlaveMasterMaster Slave

105

Figure 4.2 shows typical optical spectra of a free-running (a) and an injection-locked

F-P laser (b). The F-P laser has a multi-mode output under free-running condition with

the linewidth of each mode being about 0.1 nm. When the wavelength of the master laser

is tuned sufficiently close to one of the lasing modes of free running slave lasers and the

injection power is strong enough to create the needed injection ratio, injection-locking

can happen. In an injection-locked F-P laser, only the mode closest to the wavelength of

the master locks and all other modes are suppressed. The side mode suppression ratio is

improved from 5 dB to nearly 40 dB. Also, the linewidth of the injection locked slave

laser is reduced to 100 KHz, which is similar to the linewidth of the DFB master laser.

The injection locking between two lasers was reported by Stover and Steier in 1966.

It wasn’t until 1980 that single-mode injection-locked semiconductor lasers was realized

on AlGaAs F-P lasers by Kobayashi and Kimura [4]. Lately, optical phase modulation by

direct modulation of the slave laser current has been demonstrated. C. Henry explored the

locking range of an InGaAsP laser diode [5]. Many advantages in injection-locked lasers

have been achieved including modulation bandwidth enhancement, reduction in

non-linearities, reduction in chirp and reduction in relative intensity noise (RIN) [6-8].

4.2.2 Advantages of optical injection locking

The nonlinear coupling between carriers and photons induces the nonlinear distortion

in directly-modulated lasers. The distortions are enhanced when the laser is modulated by

106

signals with frequency components close to the relaxation oscillation frequency. It is also

known that the RIN spectrum peak coincides with the laser’s relaxation oscillation. The

injection locking can increase the relaxation frequency of the slave laser, therefore the

nonlinear distortion and RIN in few gigahertz range can be reduced and the spur free

dynamic range (SFDR) is increased as well [1, 7]. The frequency chirp is suppressed in

injection-locked lasers by preventing the laser wavelength drifting from its CW value [6].

One of the most interesting consequences of injection locking is the improved bandwidth

of the laser. The presence of the external light helps reduce the threshold of the locked

laser compared to its free running case. Based on the sublinear relationship between gain

and carrier density, the differential gain is larger if the threshold carrier density is lower.

The single mode operation and reduced linewidth increases the photon density of the

locked mode, thus stimulated emission is enhanced and the spontaneous emission is

suppressed. All these factors help to increase the bandwidth of injection-locked lasers. An

intrinsic modulation bandwidth of 35 GHz was achieved in injection –locked 1.3μm DFB

lasers [8], and under ultra strong optical injection condition, the resonance frequency of a

1.55μm VCSEL was enhanced from a free-running frequency of 6 GHz to up to 50 GHz

[9]. Jin et. al demonstrated a bandwidth of an injection-locked F-P of 10.5 GHz, which

was around twice of the free-running laser [10]. The bandwidth enhancement in QDash

F-P lasers will be studied experimentally and theoretically in this chapter.

107

Fig 4.2 The spectra of the free running and the injection locked F-P laser

-45

-40

-35

-30

-25

Inte

nsity

(dB)

1580nm157515701565156015551550Wavelength (nm)

Free running laser

-40

-35

-30

-25

-20

-15

-10

Inte

nsity

(dB)

1580nm157515701565156015551550Wavelength (nm)

Injection locked laser

108

4.3 Device description and experimental set up

4.3.1 Wafer structure and device fabrication

A quantum dash is similar to a quantum dot but elongated in one direction. QDash

lasers have similar optical characteristics with typical QD lasers [11]. The multi-mode

F-P QDash lasers used in this work were grown on an n+-InP substrate. The layer

structure is shown in Fig 4.3 and the AFM image of the QDash is shown in Fig. 4.4. The

DWELL active region consists of 5 layers of InAs quantum dashes embedded in

compressively-strained Al0.20Ga0.16In0.64As quantum wells separated by 30-nm un-doped

tensile-strained Al0.28Ga0.22In0.50As spacers. Lattice-matched Al0.30Ga0.18In0.52As

waveguide layers of 105 nm are added on each side of the active region. The p-cladding

layer is step-doped AlInAs with a thickness of 1.5 µm to reduce free carrier loss. The

n-cladding layer is 500-nm thick AlInAs [11]. The laser structure is capped with a

100-nm heavily p-type doped InGaAs layer. Four-micron wide ridge waveguide lasers

(RWG) were fabricated with 500 µm cleaved cavity lengths. The threshold current is

about 45 mA, with a slope efficiency of 0.2 W/A, and a nominal emission wavelength in

the C-band.

109

Fig 4.3 The layer structure of the 5-stack InAs QDash laser designed for 1550 nm operation.

Fig 4.4 AFM image of the QDash layer

5x

n InP substrate

n+ AlInAs (500 nm)

InAs Dashes

Al0.20Ga0.16In0.64As (1.3 nm)

Al0.28Ga0.22In0.50As (15 nm)

Al0.30Ga0.18In0.52As (105 nm)

Al0.20Ga0.16In0.64As (6.3 nm)

Al0.28Ga0.22In0.50As (15 nm)

Al0.30Ga0.18In0.52As (105 nm)

p AlInAs (1.5 μm)

p InGaAs (100 nm)

{ DWELL

110

4.3.2 Experimental setup

Figure 4.5 is a schematic of the experimental setup used to measure the modulation

properties of the injection-locked QDash lasers. The master laser is an HP 8168C tunable

laser. The light is amplified by an erbium doped fiber amplifier (EDFA) and then injected

into the slave laser. The isolators block undesired light from coupling into the master and

slave. The power meter connected to the 1/99 coupler is used to monitor the output power

of the master laser. The majority of the master laser’s output is injected into the QDash

slave laser through one of two branches of 50/50 fiber coupler. Another branch is

connected to the test arm. The optical and RF spectra of the slave laser are obtained by an

optical spectrum analyzer (OSA) and an HP 8722D network analyzer, respectively. The

DC and microwave signal is applied to the slave laser from port 1 of network analyzer.

It should be mention here that the polarization status of the traveling light was not fully

optimized in this setup even though the a polarization controller was used to provide the

highest coupling between master and slave lasers, the optical isolator is not polarization

maintaining.

111

Fig 4.5 Schematic of the injection locking experimental setup

HP tunable lasers

+ EDFA

Isolator

1/99 Coupler

Power meter

50/50 Coupler Q-dash laser

Optical Spectrum Analyzer (OSA)

Detector HP 8722D

Network Analyzer

DC+Bias T

Optical Fiber

Polarization controller

112

4.4 Bandwidth enhancement of injection locking QDash laser

The bandwidth enhancement of an injection-locked laser can be achieved by varying

the power injection ratio and detuning frequency of the master laser. The power injection

ratio is defined as the ratio of the optical power from the master injected into the slave

cavity over the total power of the slave laser: slave

master

PP

=η . The detuning is defined as the

difference in wavelength of the master and the slave laser: slavemaster λλλ −=Δ

( correspondingly, the frequency detuning is defined as masterslave fff −=Δ ). The

variation of the modulation response with different power injection ratio is shown in Fig.

4.6. The slave laser was biased at 60mA, which corresponds to a free-running output

power of about 6.5 dBm. The lasing mode was locked at 1563.70 nm. All responses were

taken at the zero detuning condition. The 3-dB bandwidth of free-running laser is 3.4

GHz. As the injection power increases, the 3-dB bandwidth increases to a maximum of

8.7 GHz at an injection ratio of -18.2 dB, which is about 2.6 times bigger than the

free-running laser.

The F-P laser has a multimode output and each mode has different intensity. It is

interesting to examine how the modulation response changes when different lasing modes

are locked because of the differential gain varies at different frequencies, then the

bandwidth should change. In Fig 4.7, the spectra of 8 locked modes and the

corresponding modulation responses are plotted. The mode #1 is the dominant mode in

113

the free-running condition and from mode 2 to 7, the wavelength of the mode increases.

The responses were taken at zero detuning and a constant overall power injection ratio of

-11.9dB condition. The 3-dB bandwidth of the injection-locked laser is increased to about

11.2 GHz. The bandwidth variation among the side modes is relatively small. Clearly, the

side mode locking variation has no significant impact on modulation response. The power

injection ratio should refer to the total slave power, not the individual mode. The results

also indicate that the differential gain does not vary significantly across the 17 nm

spectral range.

Fig. 4.6. The modulation responses of the injection-locked laser at different injection power levels.

-80

-70

-60

-50

Res

pons

e (d

B)

12108642

Frequency (GHz)

-18.2 dB -18.9 dB -19.5 dB -20.5 dB -21.9 dB -23.9 dB

Response at different injection power ratio

Free running

Islave= 60mA0 nm detuning

114

Due to One can see that a larger bandwidth enhancement occurs in the negative detuning

regime, and the modulation response is more damped on the positive detuning side

Fig. 4.7. The spectra of the free-running QDash Fabry-Perot and injection-locked laser (upper), with the corresponding modulation responses of the injection-locked laser locked at different side modes (lower).

-80

-70

-60

-50

-40

Inte

nsity

(dB)

161412108642Frequency (GHz)

#1 1565.46 #2 1555.78 #3 1558.48 #4 1560.56 #5 1562.66 #6 1567.56 #7 1569.68 #8 1572.51

Free running

-40

-30

-20

-10

Inte

nsity

(dB)

1580nm157515701565156015551550

Wavelength (nm)

1

23

4

5

6

78

#1 1565.46 #2 1555.78 #3 1558.48 #4 1560.56 #5 1562.66 #6 1567.56 #7 1569.68 #8 1572.51

-80

-70

-60

-50

-40

Inte

nsity

(dB)

161412108642Frequency (GHz)

#1 1565.46 #2 1555.78 #3 1558.48 #4 1560.56 #5 1562.66 #6 1567.56 #7 1569.68 #8 1572.51

Free running

-40

-30

-20

-10

Inte

nsity

(dB)

1580nm157515701565156015551550

Wavelength (nm)

1

23

4

5

6

78

#1 1565.46 #2 1555.78 #3 1558.48 #4 1560.56 #5 1562.66 #6 1567.56 #7 1569.68 #8 1572.51

115

The modulation enhancement can be achieved by wavelength (or frequency)

detuning. The variation of the modulation responses with different detuning are shown in

Fig. 4.8 with a fixed injected power ratio of -19.5 dB. The 3-dB bandwidth of the free

running laser is 3.4 GHz. The maximum bandwidth at -0.02 nm detuning is 8.5 GHz,

which is 2.7X larger than the 3-dB bandwidth of the free-running laser. One can see that a

larger bandwidth enhancement occurs in the negative detuning regime (The master laser

has a shorter wavelength) and the modulation response is more damped on the positive

detuning side although there is still a bandwidth increase. The same trend was reported in

Ref. [2]. In that paper, the modulation enhancement for the negative detuning case is

simulated numerically by a derived response function, however it is hard to get a clear

physical understanding out of this numerical simulation. In the next section, the response

of injection locking laser will be re-investigated using the response function of gain-lever

lasers and a more physical explanation will be given. It should be noticed that in separate

experiments done on same device [13], the injection locking map was drawn in terms of

power injection ration and detuning. The device shown in Fig 4.8 was operated at period

1, non-linear regime based on the power injection ratio and detuning condition.

116

Fig. 4.8 Modulation responses of the free-running FP laser and the injection-locked laser under different detuning conditions

-80

-70

-60

-50

Res

pons

e (d

B)

12108642Frequency (GHz)

Free running

0.02 nm

0.04 nm

0 nm -0.02 nm

-0.01 nm

Islave=60mA Injection ratio -19.5 dB

Response at different detuning

117

4.5 Injection-locking and the gain-lever

C.-H. Chang et. al. introduced a general notation for the relative modulation

response function of an injection-locked laser [2]:

H ω( )2= A 2 ω 2 + p0

2( )q.0 − q2ω

2( )2+ q1ω − ω 3( )2 (4.1)

The coefficients are given as:

( ))sincos0

0 φαφ −=SS

kp injc (4.2a)

⎟⎟⎠

⎞⎜⎜⎝

⎛−−−+= 002

11 SagSaq Spn

N ττ (4.2b)

⎟⎟⎠

⎞⎜⎜⎝

⎛++⎟

⎟⎠

⎞⎜⎜⎝

⎛−−−−−= φ

ττcos11)(

000

0

2001 S

SkSaSag

SS

kgSaSaq injc

nNS

p

injcsN (4.2c)

( )

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟

⎟⎠

⎞⎜⎜⎝

⎛−−−

+−−−=

nN

injc

injcS

p

sinjNc

SaSS

kSS

kSag

gSaSSakq

τφ

τ

φφα

1cos1

cossin)(

00

2

00

000

(4.2d)

Where Sinj and S0 are the photon density of the injected light and free-running laser

respectively, τp is the photon lifetime, τn is the carrier lifetime, g is the optical gain of the

locked laser, aN is the differential gain, as accounts for gain compression effects and α

is the linewidth enhancement factor. Ln

ckg

c 2= is the coupling coefficient and, where c

118

is the speed of light in vacuum, ng is the group index and L is the cavity length of the

slave laser. φ is the phase offset between the master and slave and can be related to

frequency detuning, Δω, as:

αα

ωφ 1

0

2

1 tan1

sin −− −⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+

Δ−=

SSk inj

c

(4.3)

The expressions in Eqn (4.2) are very complicated and it is not easy to get the clear

relationship between the various parameters. Some simplification should be done before

further investigation. The damping rate of the slave laser is

prn

Nn

fr Sa τωττ

γ 20

11+=+= (4.4a)

Where rω is angular relaxation frequency of the slave laser and rr fπω 2= . Under

the high photon density approximation, the stimulated damping term is dominant as

discussed in chapter 3, and the frγ can be expressed as:

prNfr Sa τωγ 20 =≈ (4.4b)

From the rate equation in Ref [2], the following relationship can be derived assuming

the gain compression effect is negligible:

φηφτ

γ cos2cos21

0

==⎟⎟⎠

⎞⎜⎜⎝

⎛−−=

SS

kg injc

pth (4.5)

If we define injγ as a injection rate and let it equal p0, then substitute Eqn (4.4)-(4.5)

into Eqn (4.2), we obtain:

injp γ=0 (4.6a)

119

thfrq γγ +=2 (4.6b)

⎟⎟⎠

⎞⎜⎜⎝

⎛−++= 2

22

1 2η

γγγω th

thfrrq (4.6c)

⎟⎟⎠

⎞⎜⎜⎝

⎛−+= 2

2

0 2η

γγ

τγγ th

frp

injfrq (4.6d)

The injγ and thγ are purely functions of power injection ratio and detuning, which

depend on the master laser only. The rf , τp and frγ are the characteristic parameters of

the slave laser only, their values can be extracted from the response of the slave laser

under the free-running condition or calculated using the single section response function

Eqn (3.1) in chapter 3, rf = 2.5 GHz , τp = 5 ps and frγ = 8 GHz can be obtained by

curve fitting. Now we can use Eqn (4.1) to curve-fit the experimental data in Fig. (4.8)

according to the coefficients in Eqn (4.6). The rf , τp and frγ should be fixed during

curve fitting since they are free-running parameters of the slave lasers and not affected by

external injection. The critical parameters obtained by curve fitting are listed in Table 4.1

Substituting the data in Table 4.1 into Eqn (4.6c) and (4.6d), it was found that the

last term parenthesis are much smaller than the rest of the terms in the equations. The

ratios of the last term to the other terms in both Eqn (4.6c) and Eqn (4.6d) are listed in

Table 4.1 too. It is clear that the last term can be neglected in two equations and q1, q0 can

be simplified to :

thfrrq γγω += 21 (4.7a)

p

injfrqτγγ

=0 (4.7b)

120

Table 4.1 The curve fitting results for response curves at different detuning using Eqn

(4.6) and Eqn (4.1).

Detuning （nm） γinj (GHz) γth (GHz) η (GHz) Ratio in q1 Ratio in q0

-0.02 57.84 41.28 29.22 0.0031 0.00014

-0.01 50.30 39.8 28.1 0.0043 0.002

0 40.53 38.1 24.98 0.006 0.0003

0.01 26.39 35.66 25.03 0.017 0.0015

0.02 19.48 33.81 24.68 0.020 0.0024

0.03 14.63 32.42 22.73 0.017 0.0027

0.04 12.15 31.12 21.84 0.014 0.0032

Using simplified coefficients in Eqn (4.6) and Eqn (4.7), the response equation Eqn

(4.1) can be re-written as:

( )[ ]

( ) { }[ ]232

2

2

22

2

2

ωωγγωωγγτγγ

γωτγ

ω

−++⎥⎥⎦

⎤

⎢⎢⎣

⎡+−

+⎟⎟⎠

⎞⎜⎜⎝

⎛

=

tharthap

injfr

injp

fr

H (4.8)

In chapter 3, the response function of the gain-level laser was derived under high

photon density approximation [12], which is:

121

( )[ ]

( ) { }[ ]232

2

2

22

2

2

ωωγγωωγγτ

γγ

γωτγ

ω

−++⎥⎥⎦

⎤

⎢⎢⎣

⎡+−

+⎟⎟⎠

⎞⎜⎜⎝

⎛

=

barbap

ba

bp

a

R (4.9)

It can be seen that Eqn (4.8) and (4.9) have similar forms because both of them are

used to describe the coupled oscillator system. The injection locking system can be

described by gain-lever equation under the approximation that thb γγ ≈ . Finally, the

coefficients correspondence between Eqn (4.1) and (4.9) are listed below.

p

a

ba

bar

p

ba

b

pqA

qq

q

p

τγ

γγγγω

τγγ

γ

=⇔

+⇔+⇔

⇔

⇔

0

0

2

21

0

0

(4.10)

The first important correspondence is bp γ⇔0 , it is understandable because p0 is

purely induced by the master or control laser and γb is the parameter that describes the

control section in the gain-lever, especially under strongly asymmetric pumping. P0 can

be thought of as the damping rate of the master laser.

4.4.2 Bandwidth enhancement explanation using gain-lever equation

We replace notation γ b and γ a in Eqn. (4.9) with γ inj and γ fr to indicate that they are

effectively applied to the injection-locking scheme. Eqn (4.9) can then be re-written in

terms of the frequency as following:

122

( ) 2

32

2

2

23

22

3

2

428

218

)(

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛++

⎥⎥⎦

⎤

⎢⎢⎣

⎡ +−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛

=

ffff

f

fRinjfr

rinjfr

p

injfr

injp

injfr

πγγ

πγγ

τπγγ

γπ

τπγγ

(4.11)

The new relaxation frequency of the injection-locked laser is approximately:

( )injfr

injfr

prf

γγγγ

τπ +=

121

(4.12)

Consequently, the relaxation frequency of the injection-locked laser is the geometric

mean of the photon lifetime and the parallel sum of the master and slave damping rates.

Since fr does not change at a fixed slave bias, any enhancement in the relaxation

frequency is dominated by γ inj . At a certain power injection ratio, the variation of γinj can

only be from detuning. The simulated modulation responses are plotted in Fig 4.9. The

γ inj increases from 20 GHz to 120 GHz, and the other coefficient are determined from

experimental and curve fitting data. It can be seen that the simulated response curves are

similar with experimental data with different wavelength detuning. The relaxation peak as

well as the 3-dB bandwidth increase with γ inj .

Using Eqn. (4.9), the actual value of the γ inj can be extracted from the experimental

data in Fig 4.8 and plotted in Fig. 4.10 as function of the detuning. As the detuning varies

from 40 pm to -20 pm, γinj increases from 20 GHz to 160 GHz as expected.

From Eqn (4.12), the validation of gain-lever model Eqn (4.9) to simulate period 1,

non-linear regime can be examined. As above mentioned, Eqn (4.9) is derived under the

123

high photon density approximation. At low photon density case, the two damping rate are

dominated by carrier lifetime and relatively equal to each other according to Eqn (3.12), fr

is close to a constant in Eqn (4.12) and there will no bandwidth variation. The gain-lever

model can not be applied. To enhance to bandwidth, first, the damping rate should be

dominated by the stimulated lifetime, which can be achieved in the high photon density

operation situation; second, γ inj should be significantly different from γ fr , i.e. frinj γγ >> .

(In gain-lever device, this condition requires the gain-section has higher differential gain,

which is contrary to the normal gain-lever configuration, so it is called the inverted

gain-lever.).

An interesting question is what is the maximum relaxation frequency and bandwidth

that can be achieved at a fixed injection power level? From Eqn (4.8), the maximum

relaxation frequency can be expressed under the assumption that γinj is much larger than

γfr :

p

frfrf

τγ

π21

max_ = (4.9)

Also, Eqn (4.1) can be solved to find the expression for the 3-dB bandwidth, and then

assuming that γinj >> γfr, the maximum achievable 3-dB bandwidth is approximately:

( )p

frdBf

τγ

π21

21

max_3 += (4.10)

And we find the classic relationship between relaxation frequency and 3-dB bandwidth

here: max_max_3 55.1 frdB ff = .

The γfr and τp are measured and calculated as 8 GHz and 5 ps respectively from the

124

experimental data shown in Fig 4.8. These values lead to a predicted f3dBmax of 10 GHz,

which compares favorably to the measured value of 8.5 GHz at -20 pm detuning at which

γinj is much larger than γfr To the best of our knowledge, this is the first time the

maximum bandwidth has been predicted for injection-locked semiconductor lasers.

Fig 4.9 Simulated modulation responses of injection-locked lasers using Eqn (4.1), the bandwidth incrased with γinj

2 4 6 8 10 12

-30

-20

-10

-30

10

20

Frequency (GHz)

Inte

nsity

(dB

)

Free-runnigγinj=20 GHz

40 GHz60 GHz80 GHz100 GHz120 GHz

125

160

140

120

100

80

60

40

20

γ inj (

GH

z)

40 30 20 10 0 -10 -20Detuning (pm)

Fig. 4.10 Variation of γinj as function of detuning

126

4.6 Summary

The modulation characteristics of injection-locked QDash F-P laser was studied

theoretically and experimentally. The 3-dB bandwidth enhancement was demonstrated

under different injection power ratio and frequency detuning. A maximum 3-dB ( f3dB_max)

bandwidth of 8.7 GHz was achieved at an injection ratio of -18.2 dB, and f3dB_max = 11.2

GHz was demonstrated at a higher power injection ratio of -11.9 dB, which is 4 times of

the bandwidth of the free-running laser. By comparing the modulation responses of the

injection-locked side mode of the F-P laser, it is found that the side mode locking

variation has no significant impact on modulation response. A new equation to describe

the modulation response of injection-locked laser is established, which is inspired from

the gain lever model. An analytical expression of relaxation frequency is derived, and the

maximum achievable 3-dB bandwidth at a fixed power level is predicted for the first

time.

127

References

[1]. T. B. Simpson, J. M. Liu, and A. Gavrielides, "Bandwidth enhancement and

broadband noise reduction in injection-locked semiconductor lasers," IEEE Photon.

Technol. Lett., vol. 7, no. 7, pp. 709-711, 1995.

[2]. C.-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, "Injection locking of

VCSELs," IEEE J. Sel. Topics Quantum Electron., vol. 9, no. 5, pp. 1386-93, 2003.

[3]. X.-M. Jin, S.-L. Chuang, “Bandwidth enhancement of Fabry-Perot quantum-well

lasers by injection-locking”, Solid-State Electronics, vol. 50 pp. 1141–1149, 2006

[4]. S. Kobayashi, S. Kimura, “Injection locking characteristics of an algaas

semiconductor-laser”, IEEE Journal of Quantum Electronics, vol. 16, no. 9, pp. 915-917,

1980

[5]. C. H. Henry, N. A. Olsson, and N. K. Dutta, "Locking Range and Stability of

Injection Locked 1.54 um InGaAsP Semiconductor Lasers," IEEE Journal of Quantum

Electronics, vol. QE-21, pp. 1152-1156, 1985.

[6]. C. Lin, J. K. Andersen, and F. Mengel, "Frequency chirp reduction in a 2.2 Gbit/s

directly modulated InGaAsP semiconductor laser by CW injection," Electron. Lett., vol.

21, no. 2, pp. 80-81, 1985.

[7]. X. J. Meng, T. Chau, and M. C. Wu, "Improved intrinsic dynamic distortions in

directly modulated semiconductor lasers by optical injection locking," IEEE Trans.

Microw. Theory Tech., vol. 47, no. 7, pp. 1172-1176, 1999..

128

[8]. Hwang SK, Liu JM, White JK. “35-GHz intrinsic bandwidth for direct modulation in

1.3-mu m semiconductor lasers subject to strong injection locking”, IEEE Photon.

Technol. Lett., vol. 16, no. 4, pp. 972-974, 2004

[9]. L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M.-C.

Amann, “50-GHz Optically Injection-Locked 1.55-_m VCSELs”, IEEE Photon. Technol.

Lett., vol. 18, no. 2, pp. 367-369, 2006

[10]. X.-M. Jin, S.-L. Chuang, “Bandwidth enhancement of Fabry-Perot quantum-well

lasers by injection-locking”, Solid-State Electronics, vol. 50 pp. 1141–1149, 2006

[11]. R.-H Wang, A. Stintz, P. M. Varangis, T. C. Newell, H. Li, K. J. Malloy, L. F.

Lester, “Room-temperature operation of InAs quantum-dash lasers on InP (001)”, IEEE

Photon. Technol. Lett. vol. 13, no. 8, pp. 767-769, 2001.

[12]. N. Moore, K. Y. Lau, Ultrahigh efficiency Microwave signal transmission using

tandem-contact single quantum well GaAlAs lasers, Applied Physics Letters, vol.55,

no.10, p.936-938, 1989.

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129

Chapter 5 Conclusion and future work

5.1 Summary

In this work, the techniques for improving the high frequency modulation

characteristics of quantum dot lasers were studied, including the p-doping technique in

single-section QD lasers, the gain-lever effect in two-section lasers and the

injection-locking method.

Firstly, the static performance and modulation frequency response of un-doped and

p-doped InAs/GaAs QD lasers was studied. Contrary to the theoretical predictions, the

modulation efficiency and the highest relaxation frequency of 1.2-mm cavity length

lasers decrease monotonically with the p-doping level from 0.54 GHz/mA1/2 and 5.3 GHz

(un-doped wafer), 0.46 GHz/mA1/2 and 3.6 GHz (40 holes/dot). The degradation of the

modulation performance of the p-doped device is attributed to the higher gain saturation

factor due to carrier heating effect. The internal loss increases with p-doping

concentration from 7.5 cm-1 for the 20 holes/dot wafer to 10 cm-1 for 40 holes/dot wafer,

which are much larger than the value of 2 cm-1 for un-doped lasers. Based on the

curve-fitting procedure, the saturation power is found to decrease with the p-type level

from 90 mW (un-doped) to 18.4 mW (40 holes/dot). Although the maximum ground state

gain of p-doped laser is larger than that of un-doped lasers and increases with p-doping

level, the undesired increased in internal losses induces gain saturation with carrier

130

density and gain compression. thus degrading the high-speed performance of p-doped QD

lasers.

Secondly, the gain-lever effect was studied in two-section QD lasers to increase the

modulation efficiency and bandwidth. An 8 dB modulation efficiency enhancement was

achieved using the p-doped QD laser. Due to the stronger gain saturation with carrier

density, the un-doped device shows a larger gain-lever effect over the p-doped devices. A

20 dB enhancement in the modulation efficiency is demonstrated by the un-doped QD

laser. A new relative response equation is derived under the high photon density

approximation. A 1.7X 3-dB bandwidth improvement is theoretically predicted by the

new model and realized in the un-doped QD gain-lever laser under extreme

asymmetrically biased condition. It is also demonstrated for the first time that in the

gain-lever laser, the 3-dB bandwidth can be 3X higher than relaxation frequency instead

of 1.55X in typical single-section lasers.

Finally, the injection-locked laser was realized in QDash lasers for the first time. By

varying the power injection ratio and detuning, the modulation bandwidth of the slave

laser was increased. The 4X bandwidth improvement was demonstrated in a

injection-locked 0.5-mm long QDash F-P laser. By analyzing the curve fitted data, it was

found that gain-lever equation can be used to describe the injection-locking system in the

period 1, non-linear regime. Not only the complexity of response equation of the

injection-locked laser is reduced, but also the physical meaning of coefficients in the

equation is given clearly. Based on the gain-lever model, an analytical expression of the

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relaxation frequency of a injection-locked laser is derived, and the maximum achievable

3-dB bandwidth at a certain power level is predicted for the first time.

5.2 Suggestions for future work

The p-doping technique is predicted as a promising way to enhance the bandwidth

of high-speed QD lasers. But the theoretical model did not account the side effect of

adding extra dopant, which will introduce the carrier heating effect due to increased

internal loss. The results obtained in this work shows the carrier heating effect can

severly degrade the modulation performance of QD laser because the QDs have smaller

saturation power. More complete theoretical work needs to be developed to include the

carrier heating effect. Since in this work, p-doped QDs with a doping level varies from

20-40 holes/dot were examined. These doping level are relative high. To balance the

effect of high internal loss, from the experiment side, it is suggested that studying the QD

materials with doping level from 5-20 holes/dot would be approprite.

The gain-lever laser provides a useful tools to enhance the modulation efficiency

and bandwidth. In this work, we neglect the effect form non-linear gain compression. The

full expression for damping rate should be:

001 PG

pc⎟⎟⎠

⎞⎜⎜⎝

⎛+′+=

τε

τγ (5.1)

Under extreme asymmetrically bias condition, the gain compression terms in the gain

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section could have a significant impact on the damping rate of two sections. The

gain-lever effect may disappear due to large non-linear gain compression. We already

observed that the gain-lever effect becomes weaker at very high power level. We are

trying to develop the new response model which includes the non-linear gain term. Also,

the studies on the FM modulation response of inverted gain lever QD laser can be

launched in the future and higher FM modulation efficiency enhancement is expected.

In Fig 5.1, an improved version of the setup for injection-locking QD laser is shown.

Compared to the one used in this work, the isolators are replaced by polarization

maintained (PM) circulator. The PM fiber is used in the optical path between the master

and slave laser. Therefore, the polarization status can be well-controlled in this setup and

the insertion loss is reduced too. We have already obtained much higher power injection

ratio based on this setup. The single-mode DFB laser is expected to be used as the slave

laser in the next experimental step. Not only does the lager bandwidth of DFB lasers help

to push the bandwidth of injection-locked laser even further, but also the better

correlation between injection-locked lasers and gain-lever lasers is expected since our

gain-lever model is actually derived based on single-mode operation condition. The

improved simulation model are on their way to be developed.

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Fig 5.1 The experimental setup for injection-locked QD lasers. The polarization status is carefully controlled. .

Tunable DFB laser

95/5 Coupler

EDFA

Power Meter

Polarization Controller

50/50 Coupler

OSA

Slave Laser

Network Analyzer

PM circulator

Tunable DFB laser

95/5 Coupler

EDFA

Power Meter

Polarization Controller

50/50 Coupler

OSA

Slave Laser

Network Analyzer

PM circulator